Kante has been strongly linked with a move away from the Champions.
Speculation has been gathering pace that Kante will leave the Premier League champions after just one season, with Chelsea and Juventus among those credited with interest in the France international.
They cite reports in France that a £29 million deal has been agreed between the Foxes and Chelsea for him to move to Stamford Bridge.
However, Leicester are reportedly hoping that improved terms will persuade him to stay at the club.
Kante was an integral part of the side that won the league last season. While Jamie Vardy and Riyad Mahrez were credited for their exploits in the final third, Kante's work at the heart of the midfield did not go unnoticed as he was included in the PFA Premier League team of the year for last season. His ability to break up play and cover ground was integral to the side's superb transitional play that proved so effective.
Sky cited back in March that Serie A champions Juventus were also interested in the 25-year-old.
It will represent something of a coup for Leicester to keep hold of one of their star players. They already managed to secure the services of Vardy, and seemingly Mahrez, for the coming season, but managing to secure all three will be a massive boost, especially with a season of Champions League football ahead of them.
If Kante does stay it the club, it will only add to the feel-good factor after a remarkable season last term.