The 27-year-old still has three years remaining on his current deal, but the Blues are keen to hand him improved terms in a bid to ward off interest and secure his long-term future.
Both Paris Saint-Germain and Juventus have been linked with Kante, but The Express reports that Chelsea are willing to make him one of their highest earners with an offer of around £200,000 per week.
Kante has established himself as a key member of Chelsea's midfield since joining from Leicester City in 2016, winning the PFA Player of the Year award in his first season after helping Chelsea to the Premier League title.
The France international has also been one of the stars of this summer's World Cup, playing a crucial role in helping his country to the final.
Uncertainty continues to reign over Chelsea's managerial situation, though, with Antonio Conte taking charge of pre-season training despite the expectation that he will be replaced by Maurizio Sarri before the start of the new season.