Black may have walked from an air-conditioned room in to midday heat, with the change in temperature causing her to become dizzy, the Sun newspaper reported.
A post-mortem examination is due to be carried out today, to determine the cause of death, but police in Spain have said "everything at this stage is pointing towards her death being the result of natural causes".
Spanish sources said Cilla's son found her lying on her back on a sun terrace adjoining her bedroom.
The Telegraph newspaper reports that Black's doting son Bobby discovered her body after smashing his way into her bedroom when she failed to rise from an afternoon siesta.
The legendary singer and TV presenter's eldest child broke open her door when he went to see if she was okay late Saturday afternoon and got no response.
Her sudden death at her home in the south of Spain has left friends, family and the British public in shock.
Tributes have been pouring in for Black, 72, led by close friends such as Sir Cliff Richard, Sir Paul McCartney and Christopher Biggins.
She rose to fame in the 1960s as an associate of The Beatles and their manager Brian Epstein.
Born Priscilla Maria Veronica White in
Liverpool, she became the first woman to have her own prime-time chat show on BBC1.
Cilla Black on Blind Date in 1998 with couple Emma and Bernard
Cilla Black , Petula Clark and Sandie Shaw on May 4, 1965.
Photo of Cilla BLACK; Posed studio portrait of Cilla Black (Photo by RB/Redferns)
Cilla Black with comic duo Dudley Moore right and Peter Cook in 1966.
Cilla Black with her husband and manager Bobby who died in 1999. Photo: Tony Cooke
British presenter Cilla Black poses at the premiere of "Sleuth" in London in this November 18, 2007 file photo. ReutersAnthony Harvey/Files
Cilla Black arrives for the party to celebrate the civil ceremony of British pop star Elton John and David Furnish in Windsor, southern England in this December 21, 2005 file photo. Reuters/Toby Melville/Files
File photo dated 27/11/2007 of Cilla Black attends the private view of the new 'Modern Muses' photography exhibition by Bryan Adams at The Hospital, Endell Street in London. Photo: Carmen Valino/PA Wire
British presenter Cilla Black poses at the premiere of "Sleuth" in London in this November 18, 2007 file photo. Black died on August 2, 2015 aged 72, according to national broadcaster the BBC. REUTERS/Anthony Harvey/Files
File photo dated 16/7/1997 of Cilla Black posing for the media with her OBE she received form the Queen during an Investiture ceremony at Buckingham Palace in London. Photo: John Stillwell/PA Wire
File photo dated 15/10/1995 of Cilla Black (left) and comedienne Faith Brown are entertained by Comedian Mike Yarwood at the unveiling of a plaque in honour of Bill Cotton in London. Photo: Neil Munns/PA Wire
File photo dated 14/12/1997 of Cilla Black with her Top ITV Personality Award presented at the 1997 British Comedy Awards. Photo: Rebecca Naden/PA Wire
File photo dated 5/8/1970 of Cilla Black and her manager and husband Bobby Willis and 10 day old baby on Robert John Willis as they leave the avenue clinic in St Johns Wood, London. Photo: PA Wire
File photo dated 25/1/1969 of Cilla Black and manager Bobby Willis after their wedding at St Marylebone Register Office in London. Photo: PA Wire
File photo dated 6/12/2004 of Shirley Bassey and Cilla Black arrive for the world premiere of Andrew Lloyd Webber's The Phantom Of The Opera at Odeon Leicester Square, central London. Photo: Andy Butterton/PA Wire
File photo dated 12/2/1964 of Cilla Black who has died at her home in the south of Spain, according to reports. Photo: PA Wire
File photo dated 5/8/1970 of Cilla Black with her 10 day old baby son Robert John Willis as they leave Avenue Clinic in St John's Wood, London. Photo: PA Wire
File photo dated 9/3/2004 of Michael Parkinson and Cilla Black arrive for the Bob Monkhouse BAFTA Tribute at BBC Television Centre in west London. Photo: Yui Mok/PA Wire
File photo dated 8/3/1968 of Cilla Black and Cliff Richard at BBC Television office in Shepherd's Bush, London, as they helped to count votes for Britain's song for Europe. Photo: PA Wire
File photo dated 2/11/2001 of Cilla Black during the launch of her dating show 'Blind Date', on the balcony of the Dorchester Hotel in London. Photo: Yui Mok/PA Wire
Cilla Black with Cherie Booth, Chancellor of John Moore's University in Liverpool, after she attended the presention of Cilla's honorary fellowship at Liverpool's Anglican Cathedral. Photo: Phil Noble/PA Wire
File photo dated 4/5/2004 of Paul O'Grady and Cilla Black arrive for Attitude Magazine's 10th Birthday Party at the Atlantic Bar & Grill in central London, to celebrate 10 years for the gay style magazine. Photo: Myung Jung Kim/PA Wire
File photo dated 4/8/2001 of Cilla Black, son Robert Willis and his new wife Fiona after their wedding at St Mary The Virgin Church in Denham, Buckinghamshire. Photo: Matthew Fearn/PA Wire
File photo dated 28/5/1964 of Tommy Cooper and Frankie Vaughn helping Cilla Black to celebrate her birthday. Photo: PA Wire
File photo dated 31/3/1965 of Cilla Black at London Airport where she was leaving for New York to appear on the Ed Sullivan Show. Photo: PA Wire
File photo dated 14/3/2000 of Cilla Black after she received a special award for outstanding contribution to broadcasting, at the Television and Radio Industries Club (Tric) Awards in London. Photo: Stefan Rousseau/PA Wire
File photo dated 13/10/2005 of Cilla Black arriving at ITV's 50th Anniversary Dinner at the Guildhall, central London. Photo: Ian West/PA Wire
File photo dated 2/7/2010 of Cilla Black arriving at the O2 Silver Clef Awards 2010, held at the London Hilton Hotel.
File photo dated 13/7/2010 of Cilla Black and John Madejski arriving at YOTA's sponsored launch of Mikhailovsky's Swan Lake, at the English National Opera, St Martin's Lane, London.
File photo dated 13/2/1970 of Cilla Black, voted the Top British Singer (female); Cliff Richard, voted Mr. Valentine and Best Dressed Star (male); and Lulu, voted Top Female Singer (World), Miss Valentine and the Best Dressed Star (female), during the Disc and Music Echo Fourth Annual Readers' Poll Awards - Cafe Royal, London.
File photo dated 3/5/2006 of Lionel Blair and Cilla Black arriving for the Help the Aged Living Legend Awards, at Windsor Castle, Windsor, Berkshire. Photo: Hugo Philpott/PA Wire
File photo dated 9/12/1965 of Cilla Black and Bruce Forsyth record a sketch for a Christmas show at ABC-TV's studios in Teddington.
File photo dated 17/9/2008 of Cilla Black during the Fashion for Relief show during London Fashion Week at the BFC Tent, Natural History Museum, London.
File photo dated 1/11/1999 of Cilla Black leaves the St. Mary the Virgin Church in Denham, Buckinghamshire, with her son Ben (second right) following the funeral of her husband Bobby Willis after a battle with liver and lung cancer, aged 57. Photo: Toby Melville/PA Wire
File photo dated 21/3/1964 of Brian Epstein (behind) with artists, Cilla Black, Tommy Quickly (right and Billy J Kramer appearing in his show at the Palace Theatre, Manchester. Photo: PA Wire
File photo dated 29/3/2000 of Cilla Black and Jimmy Tarbuck during the inaugural International Scouse Day, at the Sugar Reef Restaurant in London. Photo: Toby Melville/PA Wire
File photo dated 15/12/1963 of rehearsals at Alpha studios, Birmingham, for ABC's 'Thank Your Lucky Stars' programme with Brian Matthew, Cilla Black (centre), The Beatles (back), Billy J. Kramer and the Dakotas, Gerry and the Pacemakers and The Searchers. Photo: PA Wire
File photo dated 22/5/1997 of Cilla Black and her husband Bobby attending the Royal Television society awards ceremony at The Grosvener in London. Photo: Neil Munns/PA Wire
File photo dated 1/12/2012 of Elizabeth Hurley (right) with Cilla Black during the The Sportingbet Winter Festival, Hennessy Gold Cup Day at Newbury Racecourse. Photo: Phil Cole/PA Wire
File photo dated 28/2/2001 of the Prince of Wales talking to actress Wendy Richard (left) andCilla Black (centre), while attending a reception to mark the 50th Anniversary of BBC Radio 4's "The Archers" at St, James Palace, in London. Photo: Michael Stephens/PA Wire
File photo dated 17/2/2002 of Cilla Black and Christopher Biggins arriving at Claridges Hotel in London for the wedding of actress Joan Collins to Percy Gibson. Photo: Andy Butterton/PA Wire
File photo dated 21/3/2005 of Queen Elizabeth II meeting TV presenter Cilla Black (left). Photo: Kirsty Wigglesworth/PA Wire
File photo dated 11/5/1964 of Gerry and the Pacemakers are welcomed back by Cilla Black and Billy J Kramer (both on right) when they arrived in London from their American tour. Photo: PA Wire
File photo dated 31/1/2010 of Prince Harry meets Cilla Black before he plays in the inaugural Setebale Polo Cup at the Apes Hill polo club in Barbados. Photo: Arthur Edwards/The Sun/PA Wire
File photo dated 7/12/2002 of Cilla Black shares a joke with the Duke of York (left) and banker David Barchetti at Knowsley Hall on Merseyside at the start of the NSPCC winter ball. Photo: Phil Noble/PA Wire
File photo dated 3/7/2014 of Cilla Black, Sir Cliff Richard and Colin Firth in the Royal Box on Centre Court during day eleven of the Wimbledon Championships at the All England Lawn Tennis and Croquet Club, Wimbledon. Photo: John Walton/PA Wire
File photo dated 30/6/2014 of Cilla Black and her son Robert Willis arrive at the FCO building in central London, for a reception for Britain's creative industries. Photo: Philip Toscano/PA Wire
Cilla Black in London in 2009
Cilla Black at Elton John and David Furnish's joint stag party in London in 2005.
Cilla Black during the launch of a new series of her dating show Blind Date in 2001.
Cilla Black with the Special Award, alongside presenter Paul O'Grady at the Arqiva British Academy Television Awards 2014 at the Theatre Royal, Drury Lane, London. Ian West/PA Wire
Paul O'Grady and Cilla Black
Singer Cliff Richard and TV presenter Cilla Black share a joke as they sit in the royal box watching Venus Williams in action against fellow American Lindsay Davenport at Wimbledon.
Singer Cilla Black takes part in Fashion For Relief at the Natural History Museum September 17, 2008 in London, England. (Photo by Mike Marsland/WireImage)
British Entertainer and Presenter Cilla Black In London for auditions for a new series of ITV's Blind Date, which will be screened later this year. (Photoshot/Getty Images)
Her star continued to shine brightly, and she had two number ones in 1964 - Anyone Who Had A Heart and You're My World.
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In a touching tribute to her, Sir Cliff Richard said he was due to visit her at her house in Spain next week.
"Her passing away is a particular shock because despite the aches and pains we all suffer, she was always so upbeat," he wrote in the Sun.
Former Beatle Sir Paul McCartney paid tribute to her from Los Angeles, saying: "Such a shock to hear about Cilla's passing. She was a lovely girl who infected everyone with her great spirit.
"From first meeting her as a cloakroom girl at the Cavern in Liverpool, to seeing her many times since, she always had a fun-loving dignity that made her a great pleasure to be around.
"She had a fine distinctive voice and was always a bit of a laugh. It was a privilege to know and love her."
And former Beatles drummer Ringo Starr said: "I just heard the news Cilla Black has left us. She was a good friend, we will all miss her. Peace to Cilla, peace and love to the family, R&B."
EastEnders star and her good friend, Barbara Windsor, described her death as "awful".
She told the BBC: "I was only with her a couple of weeks ago. I've seen her twice in the last few weeks, a nd as always she looked immaculate. That was the thing about Cilla, she always looked spot-on. But I knew she wasn't very well, she didn't seem well."
Windsor added: "I liked her, we got on well. She was nothing like me in personality at all, but she was a good, good all-round performer."