The Spain international's future with the Red Devils continues to be called into question, with Dean Henderson emerging as a genuine contender for the number one position at Old Trafford.
A recent report claimed that Henderson is expecting to be Man United's first-choice stopper next term, fuelling suggestions that De Gea could be on his way out of the club.
According to The Sun, PSG are keeping a close eye on developments in Manchester and are planning to launch an offer during this summer's transfer window.
The report claims that the French champions are prepared to match the 30-year-old's current £375,000-a-week contract and also offer a generous transfer fee to Ole Gunnar Solskjaer's side.
However, the Ligue 1 side's head coach Mauricio Pochettino is said to favour a move for De Gea, who is currently in Spain following the birth of his first child.