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.
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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.
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