The midfielder is out of contract in June, but negotiations have gone well and the two parties are finalising the details over a new three-year contract that will run until June 2026, sources added.
Kante had wanted to stay at Chelsea all along, with sources saying he is happy at the club despite the injury problems he's dealt with over the last two years. Under-fire manager Graham Potter and the new owners were also keen to keep him and the discussions saw a breakthrough at the end of January.
However, the 31-year-old has been out with injury since August, meaning he also missed the World Cup with France, but he is now training with the squad and is ready to return to first-team action. His work rate and experience will add strength and balance to a team in sore need of a boost.
Potter will also welcome the return of Kante to his injury-hit side after learning Tuesday that Thiago Silva will be out for six weeks with ligament damage in his knee. The Brazil international joins Christian Pulisic, Cesar Azpilicueta, Edouard Mendy and Armando Broja on the injured list.
The 10th-place Blues will look to end their six match winless run against relegation-threatened Leeds United on at Stamford Bridge on Saturday before hosting Borussia Dortmund next week in their Champions League round-of-16 second leg after having lost the reverse 1-0 in Germany.