The paper claim that all three sides have been impressed by the Frenchman's performances, which have seen him win an international call, and play like the best defensive midfielder in the Premier League.
Leicester paid £5.6 million to sign him from Caen last summer, and The Mirror claim they want to sign him to an improved and extended deal to ward off interest from rival clubs.
The Foxes are currently top of the league and appear set to qualify for next season's Champions League, which would mean 10th placed Chelsea may have a tough task in tempting him away in the summer.
Arsenal and Tottenham may be a different matter, and it would depend on how much either club would be willing to front up in terms of a bid.
Neither side are prolific spenders, each choosing to solve their own defensive midfield issues with internal solutions, Francis Coquelin and Eric Dier.
Kante has proven himself this season as a player of huge value, and if there was a chance either North London club could land him at a reasonable price, it would be worth considering.
With huge money available from Premier League and Champions League television deals, either Spurs or Arsenal could consider it shrewd to offer £25 million to Leicester and see if they can be persuaded to sell at a big profit.