Francois Hollande has been having an affair with Julie Gayet for two years and was introduced to her by Segolene Royal, the mother of his children, according to 'Closer' magazine.
The French president's "turbulent romance" with Ms Gayet began in 2011, before his election campaign, according to the magazine, which first reported the alleged affair.
Meanwhile, Europe-1 radio reported that Ms Gayet told the radio station by telephone that rumours she was pregnant were untrue. The actress has not spoken publicly about the matter, and her agent and lawyer have declined to comment.
Mr Hollande (59) visited his partner Valerie Trierweiler for the first time since she was taken to hospital last week after reports of the affair emerged.
Mr Hollande's office said Ms Trierweiler (48) had experienced a "crisis of nerves" on learning of the report in 'Closer' magazine last week.
The initial story showed photographs of Ms Gayet (41) and a man in a helmet it said was the president entering a flat near the Elysee Palace on December 31. It reported yesterday that the couple had initially used a vast apartment, but had abandoned it after the concierge tried to take a photograph of them. They also met at her converted loft, it said.
After a break last spring, when Ms Trierweiler became suspicious, the affair resumed in June, 'Closer' reported. A small apartment in the Rue du Cirque, 150 yards from the Elysee, became available.
"From that moment onwards, the head of state and the actress were constantly together, visiting the apartment around 20 times."
There is no love lost between Mr Hollande's four children and Ms Trierweiler. They refused to speak to her for a year after she tweeted support for a dissident Socialist running against Ms Royal in elections.
Ms Royal announced her split with Mr Hollande on the day she lost her presidential bid in 2007, but his relationship with Ms Trierweiler had been ongoing for at least two years. (© Daily Telegraph, London)