They have acted to deter interest from Paris Saint-Germain in the midfielder who impressed at the World Cup, where he helped France to lift the trophy.
Kante has been offered a new five-year contract reportedly worth a club-record £290,000 a week, nearly double his current salary of £150,000.
The 27-year-old will earn £15m per season until 2023.
The former Napoli boss joined the Stamford Bridge outfit a few weeks ago bringing Jorginho with him.
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Barcelona eyes Arturo Vidal: It all started as a tease from the midfielder's son and his YouTube channel, but more outlets have reported on a possible move to Spain. He won the title with Chelsea in his debut season at the club while helping them to FA Cup success last season.
Mina has been linked with United after starring for his country at the World Cup in Russian Federation this summer, but it would take a fee of around £30m to prise him from the Nou Camp despite the 23-year-old being out of favour in Catalonia. After the tournament, his worldwide teammate Kylian Mbappe, who plays for PSG, confessed to trying to convince Kante into making the switch to the Parc des Princes.
Hazard and fellow Belgian Thibaut Courtois, who is also believed to be subject of a £35.5-million bid from Real Madrid, are due back in training this weekend after their holidays following Belgium's run to the World Cup semi-finals.
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. Chelsea hope that mega-money offers would convince both of their key players to remain at the club. In the current Chelsea squad, Eden Hazard is the highest earner with a £220,000-a-week deal which expires in June 2020.