De Gea has a year left on his contract and negotiations over a new long-term deal have stalled. United have privately insisted they will not cash in this summer but there are fears their resolve will be severely tested by a big-money move from PSG.
Buffon will leave the Ligue 1 champions a year after arriving from Juventus, leaving coach Thomas Tuchel with just Alphonse Areola as his senior goalkeeper. Buffon and Areola shared goalkeeping duties last season.
De Gea has also been linked with Juventus and Real Madrid but sources have told ESPN FC that United fear PSG pose the most serious threat. There are doubts about whether Juventus could afford the deal while there is a belief at Old Trafford that Real Madrid's transfer priorities lie elsewhere.
PSG, who are also interested in Keylor Navas, have the funds to tempt United with a large fee and offer De Gea a lucrative wage packet while giving the 28-year-old the chance to win trophies and challenge for the Champions League.
United have been in contract talks with Spain's No.1, whose form dipped sharply during the second half of the season, for more than a year but terms have not been agreed and he could walk away for free next summer.
De Gea, who is open to staying at the club, has been offered a five-year deal worth £350,000-a-week but an agreement is yet to be reached.
He also entered the last year of his deal in 2015 and was on the brink of joining Real Madrid before the transfer broke down at the last minute.
Manager Ole Gunnar Solskjaer would also be open to handing Sergio Romero the No.1 spot while there are also high hopes for 22-year-old Dean Henderson, who helped Sheffield United secure promotion to the Premier League during a loan spell at Bramall Lane last season.