Foot Mercato reports the Blues have "absolutely no intention" of handing him a new deal.
The 31-year-old's injury record means Chelsea are reluctant to pin him down to an extension, with Kante earning a reported £170k-a-week on his current deal.
But the French World Cup winner is intent on staying in London.
As a result, his agents have offered him to both Arsenal AND Tottenham.
He is available for nothing at the end of the campaign, and free to begin talks with overseas clubs from January regarding a pre-contract agreement.