Antonio Conte is keen to strengthen his midfield, and along with Kante, has been pursuing moves for Andre Gomes and Radja Nainggolan.
But according to the Daily Telegraph, Leicester aren’t going to give up on Kante without a fight.
The report suggests Leicester are hoping to make him the highest paid player at the club, which in turn could persuade him to stay.
It is thought the reigning Premier League champions will up their contract offer, although it is unclear how much this will be.
Kante has been afforded a break after his participation at Euro 2016 with France.
Jamie Vardy has already verbally agreed a new £100,000-a-week deal with the east Midlands outfit, while talks are ongoing over new deals for Danny Drinkwater and Kasper Schmeichel.