The French giants are desperate to end their wait for a Champions League trophy and see the 28-year-old as the perfect addition in their quest to go all the way in Europe.
Chelsea would be loathe to lose one of their most important players however, particularly as they currently have a two-window transfer ban, and would demand a huge fee for the midfielder who signed a new five-year contract with the club in November 2018.
The Daily Mirror have reported that PSG will press on in their attempts to land the France international regardless, having shelved plans to bring in Evertons Idrissa Gueye who they tried to sign in January.
Despite Kante being on a reported £290,000 a week, it has been claimed the Ligue 1 champions would be willing to increase his wages in a bid to lure him to the French capital.
Since joining Leicester City from Caen as a virtual unknown in the summer of 2015, Kante has enjoyed a remarkable rise, winning two Premier League titles as well as the World Cup with France and PSG are keen to add his experience to their squad.
If Les Parisiens are unable to complete a deal for the Chelsea man then they are set to turn their attention to Watford midfielder Abdoulaye Doucoure.
The Hornets star has four years left to run on his current deal at Vicarage Road but has expressed a desire to play Champions League football and PSG have the money to make Watford an offer for the player they would find very difficult to refuse.