It is unclear how much Chelsea have agreed to pay the Premier League champions as The Guardian reported that it was about £29.2 million, while Sky Sports claimed it was around £32m.
Leicester had offered Kante a new four-year deal before he represented France at Euro 2016, but his brilliant performance last season captured the attention of many clubs, and he is now set to move to Stamford Bridge.
It is understood that the 25-year-old will undergo a medical over the weekend and meet up with Chelsea during their pre-season training camp in Austria in order to discuss personal terms.
Leicester manager Claudio Ranieri is eager to see Kante stay at the King Power Stadium, but conceded he may not get his wish.
“I don't want to lose him,” he said. “I don't want to, but I could understand if he wants to go.”
If Kante completes his move to Chelsea, he will be the first Leicester star to leave the club after their fairytale season.