De Gea has repeatedly been linked with a move away from Old Trafford, with Real Madrid well-known admirers of the stopper.
The 26-year-old nearly sealed a move to the Bernabeu two years ago, only for a faulty fax machine to ruin his dream transfer.
Real could face stiff competition for the Ligue 1 side if reports are to be believed.
French news outlet Le10 Sport claims that the Paris outfit are looking to make De Gea their next big money acquisition.
Current keepers Kevin Trapp and Alphonse Areola have failed to to impress PSG chiefs with their performances.
Atletico Madrid stopper Jan Oblak has been mentioned as a alternative target if a deal for De Gea fails to materialise.
Oblak’s current deal with Atletico has a €100million release clause, but PSG would not bulk at such a figure considering their spending last summer.
De Gea in comparison does not have a release clause included in his contract and PSG’s director of football Antero Henrique is said to have already talked to De Gea’s agent Jorge Mendes about the goalkeeper.