Kante has been one of the Foxes best performers this season as they have launched an improbable challenge for the Premier League title - with Leicester five points clear at the top with eight games remaining.
The 24-year-old signed for Leicester last summer for a fee of £5.6 million, but Chelsea would like to sign the player for potential new manager Antonio Conte, and could see him as a key part in rebuilding the side, the report states.
However, one would question the timing over whether Kante would want to leave the King Power Stadium given that they are nailed on for Champions League football next season, while Chelsea have had a disastrous season - resulting in no silverware, and are currently 10th in the Premier League table.
Though he may not have had the praise that Jamie Vardy and Riyad Mahrez have had this season, it's hard to underestimate the importance and influence that Kante has on the current Leicester side both in the way he can dictate the play, and the sheer amount of ground he can cover in a game.
Of course, it is of little surprise that clubs with open chequebooks are now sniffing around Leicester's top talent, and it could be a summer of keeping hold of their best players. But with their players on the brink of history, and playing in Europe's top competition next season, they have plenty of incentive for sticking around.