The star 'keeper is yet to commit his long-term future at Old Trafford as European clubs begin to monitor his situation.
The Red Devils have triggered a one-year extension in his contract, keeping him at the club until the end of next season.
And it's believed United have made De Gea's contract situation a priority as they fear losing their star man.
But the Ligue 1 champions are favourites at 9/2 to sign the Spaniard before the January transfer window slams shut.
Surprisingly a move to Juventus is second in the bookies' eye ahead of a return to Spain.
Betfair: Clubs to sign David De Gea before Feb 1 2019
It has previously been reported in the past of De Gea's desire to return to his home nation.
Joe Dyer of Betfair said: "PSG have only conceded six goals in nine Ligue 1 fixtures this season but they lead the charge at 9/2 to sign De Gea following the Manchester United stopper’s refusal to sign a new contract at Old Trafford.
"But the Spaniard will be able to choose from his pick of Europe’s biggest and best clubs according to the odds with Juventus 17/2, Barcelona 16/1 and the Madrid giants both 22/1.”
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