Kante "50:50" for Europa League final against Arsenal
Kante has been struggling with the problem since the weekend but Chelsea will give him until the last minute to prove his fitness for the match at the Olympic Stadium in Azerbaijan's capital.
"Kante has a very little problem with his knee. The problem is the timing, but we are trying," said Sarri.
When asked what odds he would put on Kante being available, the Italian added: "I think 50/50 at the moment. Yesterday 60/40 for the no. He was a little bit better this morning, but 50/50."
Kante has not played since coming off with a hamstring injury in a 3-0 win over Watford on May 5. He missed the second leg of their Europa League semi-final against Eintracht Frankfurt as a result, and also missed the trip to Leicester City on the final day of the Premier League campaign. That was two and a half weeks ago, and his latest problem was picked up in training at the weekend before Chelsea flew to Azerbaijan on Tuesday.
Chelsea are already without the injured Ruben Loftus-Cheek as well as Callum Hudson-Odoi for the game.
"We are in trouble with the midfield, at the moment we have only three midfielders for three positions," Sarri added. "He is the only defensive midfielder that we have so for us Kante is very important. I hope to recover him because I know very well that without N'Golo it's a problem."