PSG have a big interest in seeing the Paris-born midfielder have a homecoming, as his status with the national team grows ahead of the World Cup.
Their recent transfer business that includes both Nemyar and Kylian Mbappe, who they will formally buy this summer after an initial loan move from Monaco, leaves them at risk of falling foul of the Financial Fair Play rules set by Uefa.
The club's officials had an audience with UEFA at their headquarters on 20 April to find out more, but the restrictions mean that they will have to sell players of at least equal value to Kante, as Chelsea would likely refuse even having conversations with the Ligue 1 champions without bids of around £100m.
Mbappe was one of last season's a marquee signings for the oil rich PSG and he reveals that he was excited by the links for his club to his national team colleague.
"Kante, in terms of our needs and also the quality of the player," Mbappe told beIN Sports when questioned about which player he would like to see at the club. "I think he's a player who'd suit our team perfectly.
"He's French, and bringing a Frenchman back would be good as far as the attractiveness of our league is concerned. I think all the French love N'Golo Kante, and it would be a pleasure to see him again in our league."
The January free transfer of Lassana Diarra to PSG was made in anticipation of problems with FFP, as the club prepares to make at least one major sale.
Kante won the PFA Player of the Year last season, as he secured back-to-back titles upon moving to the Premier League with Leicester City and Chelsea.
PSG have also made first contact over Chelsea's goalkeeper Thibaut Courtois , but it remains to be seen whether they will make a formal approach.