The rather improbable move is reported by Sport, who claim that Mbappe is happy to join Chelsea but only for one year.
Mbappe has agreed to join Real Madrid on a free transfer in 2024 so would be content to play for another club until then after being frozen out of the PSG squad.
But Sport adds that Chelsea are unlikely to accept signing Mbappe for just one year, and neither will PSG.
Duncan Castles reported last weekend that Chelsea owner Todd Boehly had opened shock talks to sign Mbappe.
Castles claimed that Boehly has held direct negotiations over the deal with PSG president Nasser Al-Khelaifi
The journalist reported that Chelsea are offering a cash-plus-player deal to PSG, although it is not clear who the players in the exchange would be.
It is widely accepted that Mbappe already has a deal in place to join Real Madrid on a free transfer when his PSG contract expires in June 2024.
Only last week he refused to negotiate terms with Al Hilal, who had a €300m offer accepted by PSG.
PSG want to sell Mbappe
PSG have transfer listed Mbappe and are determined to sell the French superstar this summer in order to avoid losing him on a free transfer next year.
Mbappe has been exiled by PSG, who have excluded him from their summer tour of Japan and made him train with other transfer listed players.
PSG have made it clear to the 24-year-old attacker that he will be sold this summer – and may not play again for the club – unless he renews his contract.
Real Madrid and Chelsea are not the only big clubs who are in the race to sign Mbappe this summer.
Manchester United, Tottenham and even Liverpool themselves have been linked, although any move to these three clubs appears unlikely.
Indeed, unless PSG can come to an agreement with Madrid to sell him a year early, it appears that Mbappe will wait things out and join on a free in a year.
