The French midfielder - who has won the Premier League, the Champions League, the Europa League and the FA Cup with the Blues - has just one year left on his current deal at Stamford Bridge.
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Since joining in 2016 from Leicester City, Kante has cemented himself as a fan favourite and regular starter - and new owner Todd Boehly is keen to secure his services.
But the Blues midfielder isn't happy with the terms of the potential new deal Chelsea are currently offering, according to The Athletic.
It's understood the west London club have given the 31-year-old a new verbal offer of a two-year deal, with the option to extend for another season.
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The issue for Kante lies in the length of the proposed deal, with Chelsea's former regime led by Roman Abramovich offering him a longer offer - three years plus an option for a fourth.
Meanwhile, Kalidou Koulibaly - who is Kante's age - signed a four-year deal in July.
Should the midfielder opt to not extend his stay at the Bridge, it's also understood that two other English clubs will look to snap him up, with one side each in Spain, Germany and France also interested.
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Kante's 'injury rate' was cited by now former Chelsea boss Thomas Tuchel as a reason why terms of a new contract had been weighed up for some time.
The midfielder made 42 appearances in 2021/22, however he still had minimal time on the pitch.
He's also missed five of Chelsea's seven games this season due to a serious hamstring injury.