Kante was injured while on international duty with France and initial fears are that he will be out for up to four weeks.
That could see Kante seven matches, up to an including the home Premier League game against Manchester United on Sunday, November 5th.
Blues boss Antonio Conte says he hopes for better news on one of Chelsea’s key players.
“We are going to do a scan next week to check his situation,” Conte added. “He is improving for sure his hamstring problem.
“But this is a big loss for us because I know very well the importance of Kante in our team. We don’t have another player with the same characteristics.”
Summer signing Danny Drinkwater is also unavailable as he is still recovering from a calf injury.