Goal understands the World Cup-winning midfielder has been offered more than Eden Hazard's current £200,000-a-week contract, as they aim to convince one of their star players to shun interest from abroad.
Kante still has three years remaining on his current deal but the new contract would see him more than double his salary - a figure that currently stands at £120,000-a-week.
Despite the admiring glances from elsewhere, Goal understands Kante remains happy at Chelsea and the club's failure to qualify for the Champions League has not prompted him to consider his future.
Barcelona are another club to have shown an interest in Kante but he is an unrealistic target for the Catalans at this stage.
The Frenchman is simply out of Barca's price range given Chelsea are likely to value him at over £100 million ($131m) and are unwilling to entertain any offers.
Kante is still away on holiday after taking three weeks off following his World Cup exertions.
The Blues midfielder is due back on August 6 and will take part in a week of pre-season training before Maurizio Sarri's side's Premier League campaign kicks off on August 10 against Huddersfield Town.
As well as the 27-year-old, Chelsea have deals on the table for both Hazard, with a £300,000-a-week offer that would eclipse Kante's proposed new deal, and Real Madrid-linked Thibaut Courtois.
Callum Hudson-Odoi has also been offered a new five-year deal as the Blues aim to tie down one of their brightest young talents.