Kante is coming off a brilliant 2015/16 season in the English Premier League, where he helped Leicester City to their maiden title, with some energetic displays from midfield.
The likes of Arsenal, Chelsea, PSG, Real Madrid and recently Shanghai SIPG have all expressed an interest in the French international, but the Foxes are keen to hang onto the 25-year-old and have offered him a new R1,9-million-a-week contract to stay at King Power Stadium.
Chinese Super League club Shanghai SIPG, though, have made it clear that they are willing to offer a lot of cash both to the player and the club.
However, Chelsea believe they are in the driving seat and The Telegraph reports they "want to push the deal forward this weekend" with an offer of R550-million [£29million] already on the table.
The paper adds "Antonio Conte, the new Chelsea manager, has made his move for the player, with a formal offer being considered by the Premier League champions".