Blaise Matuidi has been heavily linked with a move away from PSG and Jose Mourinho could bring him to Man Utd if Paul Pogba stays at Juventus.
Matuidi is Manchester United's fallback target should Pogba decide against signing for the club.
Paris Saint-Germain midfielder Matuidi, 29, and Pogba share the same agent in Mino Raiola, who clinched his second summer transfer with United on Wednesday when Henrikh Mkhitaryan's move was announced.
Matuidi is out of contract at the Parc des Princes in two years' time and has been heavily linked with a move away from the Ligue 1 champions in recent days.
PSG completed the signing of Grzegorz Krychowiak from Sevilla at the weekend, while Hatem Ben Arfa also moved to the Parisians to intensify competition in a midfield that already includes Marco Verratti, Thiago Motta and Adrien Rabiot.
United are understood to be confident of agreeing a transfer fee with Juventus for Pogba, who Jose Mourinho prioritised as the 'captain' signing to reinforce the team's central midfield.
Mourinho vetoed a move for Miralem Pjanic last month in order to prioritise Pogba. Pjanic moved to Juventus from Roma in a £25.4million deal that could ultimately work to United's advantage.
It is understood that Raiola has advised Pogba to re-join United, and the Dutch agent is expected to have further talks with Pogba after France's Euro 2016 campaign. Raiola is believed to have promised United he will do his utmost to convince Pogba to sign for them.
Mourinho confirmed that he wanted to strengthen four positions during his maiden press conference on Tuesday, where he all but admitted the club's efforts to sign Pogba.
"We made a nucleus of four priorities, four positions, priorities," he explained. "To give a certain balance to the squad, to give a certain push in terms of quality, and the qualities that I need, that I want, as we know especially with the ones with more vision."
Mourinho was initially pessimistic about United's chances of signing Pogba amid intense competition, but the club's discussions with Raiola have been positive.
Matuidi and Pogba have lined up alongside each other throughout France's Euro 2016 campaign.
The future of Juan Mata looks increasingly uncertain but Mourinho risks upsetting his players if he decides to sel the Spanish playnaker.
Mata, who was sold by Mourinho to United in January 2014, is well liked among his teammates and his departure would be unpopular inside the dressing room.
Mourinho appeased the United squad before he met them by offering vice-captain Michael Carrick a contract extension weeks after his appointment was confirmed.
United players arranged a get together two days following the FA Cup final in Carrick's honour, since they were uncertain about his future, but Mata's United career was plunged into further doubt by Mkhitaryan's arrival.
Mata operated mainly on the right for United last season - wh ich is where Mkhitaryan excelled for Borussia Dortmund. Jesse Lingard and Adnan Januzaj have also played their best football for United on the right flank while Mourinho praised Mkhitaryan's 'change of speed with the ball and without the ball'.
Mata was named Chelsea's player of the year in his first two seasons at the club before Mourinho returned in 2013 and marginalised the playmaker.
Mata reacted angrily when he was substituted in his last Chelsea game at Southampton in January 2014 and signed for United three weeks later for £37.1million.
The Spain international was omitted from Vicente del Bosque's Euro 2016 squad and was believed to be hopeful United would look to an alternative to Mourinho.
However, Mata is believed to be happy to stay at the club.
Meanwhile, the make-up of Mourinho's backroom staff has been confirmed. Trusted lieutenant Rui Faria has become the Red Devils' assistant manager.
Mourinho first met Faria at Barcelona before he worked as Mourinho's fitness coach during his time in charge of Uniao de Leiria in Portugal and followed him to Chelsea (twice), Inter Milan and Real Madrid.
Coaches Silvino Louro, who has been with Mourinho for more than a decade having started out as his goalkeeping coach, Ricardo Formosinho and Carlos Lalin - who also have previous experience working with the Portuguese - and Emilio Alvarez have all been confirmed as members of the coaching staff along with analyst Giovanni Cerra.