The duo both shone at the World Cup in Russia, as Didier Deschamps men avoided a repeat of their Euro 2016 heartache by beating Croatia 4-2 in the final.
Since the tournament ended, Kante has been heavily linked with a move to PSG, as the French outfit look to build a side capable of winning the Champions League.
And Ligue 1 star Mbappe has admitted he has tried to persuade his fellow countryman to return to France.
“I told him [Al-Khelaifi] again that Kante would be good for our team,” he told France Football.
“I spoke to N’Golo during the World Cup but without abusing because I know what it is when you wash your brain with transfers.
“In the end, I just put a few words in his pockets, which he must have discovered once he returned home, to get the message across.”
New Chelsea boss Maurizio Sarri will no doubt be keen to keep hold of Kante, despite bringing in central midfielder Jorginho earlier this month.
But French football expert Julien Laurens admitted after the World Cup the former Leicester man has always had his heart set on a move to Paris.
“He’s a Paris born-and-bred kid and I think he always at some point wanted to go there,” he told the BBC World Cup transfer podcast.
“He could have gone there and chose Chelsea instead, which I think he would agree now was the right move for him at the time.
“And now they need a player like him and Tuchel loves him and they are going to try it.
“I’m not sure it will be enough, but they will try.”