The Blues are said to have turned their attentions to the Foxes' defensive midfielder while they also continue negotiations with Roma over midfielder Radja Nainggolan.
The France international took many by surprise in Leicester's title-winning campaign, and not only was he being considered amongst the top-performing new signings in the Premier League, but his performances also saw him garner a great deal of attention from top clubs around Europe.
The 25-year-old has previously been linked with moves to Arsenal and Juventus, with Chelsea most recently said to be seriously looking to add the player to their books ahead of the 2016/17 campaign.
Kante was instrumental in helping Leicester lift the title, making 37 league appearances and averaging an impressive 4.7 tackles and 4.2 interceptions per match.
If the Frenchman does make the move to Stamford Bridge, he will be competing with the likes of Kurt Zouma, Nemanja Matic and Jon Obi Mikel for a starting berth.