De Gea is unsettled at Old Trafford and is about to enter the final year of his contract.
It was previously claimed he would seek a summer move if they failed to qualify for next season’s Champions League and United did just that after last weekend’s disappointing 1-1 draw with Huddersfield.
United boss Ole Gunnar Solskjaer has always said he wants to keep De Gea beyond his current deal but they could now be forced to sell or risk losing him for nothing at the end of next term.
And Canal+ reporter Garetier says PSG have tried to capitalise on the situation with an early offer.
“Paris Saint-Germain are seeking a world-class goalkeeper now more than ever,” he said.
“The club have made an offer for David de Gea.”
PSG are desperate for a new man between the sticks as Gianluigi Buffon has recently turned 41.
Boss Thomas Tuchel has rotated the veteran stopper with Alphonse Areola all season and previously admitted they need to find a more permanent solution.
“We can’t go on like this, we’re the first club in the history of football to do it, it’s not possible,” he said.
De Gea would be a ready-made No 1 but has struggled for form at times this season and made a number of high-profile errors.
Despite that, he is expected to play when United take on Cardiff in their final game of the season in Sunday and Solskjaer threw his support behind him after a recent mistake against Manchester City.
“David has been unbelievable for this club,” the Norwegian said.
“We support each other. There is no chance anyone can blame him for losing points.
“He knows he could have had that shot, but that is football.
“David likes to play games. I will have chats with him and he will respond in the right way.”