Mbappe recently turned down a world record bid of £259m from Saudi Pro League club Al-Hilal to join them for one season.
Mbappe was in talks with Liverpool over a possible transfer before opting to join PSG in 2018 and has always been very complimentary of Jurgen Klopp’s side.
“We talked a little bit, but not too much,” he told the Telegraph last year.
“We talked a little bit. I talked to Liverpool because it’s the favourite club of my mum, my mum loves Liverpool.
“I don’t know why, you will have to ask her! It’s a good club and we met them five years ago. When I was in Monaco I met them. It’s a big club.”
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PSG are not willing to let Mbappe go for free next summer without recouping funds for the player first.
Mbappe has already told the club he won’t trigger a 12-month extension on his contract, which expires at the end of next June. He has until Monday to change his mind and sign the extension, but that looks increasingly impossible.
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Mbappe has already made it clear he intends to play only this season with the French champions, and then leave. That means he could join long-time suitor Real Madrid for free. With no transfer fee involved, Madrid can offer him a lucrative signing bonus and a massive salary.