According to Le10Sport, PSG are willing to offer Kante a deal worth between €12m and €15m each season to tempt him back to his native France.
That equates to a maximum weekly salary of up to £255,000.
It has been rumoured since the end of the season that Kante is considering leaving Chelsea this summer, while the player himself has so far refused to clarify his club future as a result of wishing to focus on playing at the World Cup with France.
Kante was once more vital as Les Bleus beat Belgium on Tuesday night to reach the final, showing just why PSG are seemingly so keen to sign him - in that respect, Le10Sport have called the former Leicester man PSG's 'summer priority'.
Kante still has three more years left on his current Chelsea contract but the Daily Express claims that talks over an improved new deal are already underway in light of PSG's interest.
The story explains that Chelsea want to tie Kante down to a new five-year contract until 2023 worth £200,000-per-week. That figure would make him one of the club's top earners.
With the managerial situation still up in the air, Chelsea are already worried about a potential exodus this summer, with Thibaut Courtois, Eden Hazard and Willian among those heavily linked with high profile moves away from Stamford Bridge.