Kante's contract with the Blues runs until next summer and there have been no talks over a new deal.
The French midfielder would like to stay at Stamford Bridge but there is little chance that he will remain with the club.
If Kante does leave Chelsea, he would like to remain in London, which brings Arsenal and Tottenham into the equation.
The two north London rivals are the clubs in the English capital which boast the most ambition domestically and in Europe.
Prior reports have claimed that Paris Saint-Germain are interested in the midfielder but Kante is said to be against a move to the Parc des Princes.
The former Leicester City man has run into injury issues at the start of the season which has seen him miss eight games for Chelsea.
He has made just two appearances so far this season and is yet to play under new Blues manager Graham Potter.
The Frenchman has been at Stamford Bridge for seven seasons, making 262 appearances, winning the Champions League and the Premier League title as well as the Europa League.
Darren Bent wants Arsenal to sign Chelsea's Kante as a free agent next summer
Former Tottenham Hotspur striker Bent wants the Gunners to move for the French midfielder if he becomes a free agent in 2023.
The Arsenal supporter told talkSPORT:
“Even at 31 years old, he’s on a free at the end of this season, I would take him."
“I don’t think it would ever happen because for what (Mikel) Arteta’s trying to build, Kante is too old. But look at what he can give you, not as a starter, but someone who’s just in and about the squad. Imagine him and Partey…he is fantastic, he’ll go down as one of the absolute greats."
Bent continued to suggest the Gunners signing Kante by claiming there will be a queue for the Frenchman:
“If Kante is on a free at the end of this season, there will be top teams around the world that will still be queuing up for his signature.”
Arteta's side do have a history of signing former Chelsea talent. They signed David Luiz from the Blues for £7.8 million in 2019.
The Gunners also lured legendary goalkeeper Petr Cech to the Emirates Stadium from west London for £12.6 million in 2015.
Willian also moved to Arsenal as a free agent after a spell with the Blues in 2020.