The goalkeeper is out of contract at the end of the season and is believed to be stalling on a new deal.
Juventus are believed to be interested in signing the Spaniard, who is regarded as one of the best shot-stoppers on the planet.
Real Madrid have been long-term admirers of De Gea though brought in Thibaut Courtois from Chelsea during the transfer window.
And the Mail now claim PSG are favourites to sign De Gea, making him the highest-paid goalkeeper in the world.
It’s reported that he would sign a deal worth £300,000 per week and an overall salary of £15.5million.
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Real Madrid could benefit from PSG signing De Gea with the Ligue 1 giants under Financial Fair Play restrictions.
It could mean they sell Neymar to Los Blancos, with it been reported that Real Madrid are keen on the Brazilian.
That would free up funds for PSG to make a move for De Gea and they would likely build their team around Kylian Mbappe.
Manchester United boss Jose Mourinho has been vocal on De Gea’s United future, with the Special One revealing he isn’t confident of keeping the Spaniard at Old Trafford.
“I am not confident,” he recently said.
“I cannot find the word in English, but let’s see what happens.
“Only the club, David and his people can answer that.
“My comment is only that everyone knows how good he is, how important he is for Manchester United and, if the club want to be better than it is and not worse, obviously it would be very important to keep David.”
De Gea kept a clean sheet as United were held to a goalless draw by Crystal Palace on Saturday.
The Red Devils are next in action in the Champions League, hosting Young Boys on Tuesday (8pm).