The French star will be given every chance to prove his fitness, but the game in Baku may come too soon as the Blues deal with several injuries in midfield.
In training on Tuesday, Kante spent nearly the entire open session training alone with a fitness coach and then went down the tunnel before the rest of his team-mates.
Sarri has said that the injury, which was suffered in training on Saturday, is not serious, but the 28-year-old still may be forced out of the match at the Olympic Stadium in Azerbaijan's capital.
"Kante had a little problem on Saturday, a very little problem within his knee," Sarri told a news conference on Tuesday.
"The problem is the timing because we had only four days. We are trying. It's not really a very serious injury. We have the problem of the three or four days to try and recover him.
"At the moment we don't know. We will try. We will try to the last moment, so we will try tomorrow. But we don't know at the moment."
When asked to asses Kante's chances of playing, Sarri said: “I think it's 50-50 at the moment. Yesterday, 60-40 for 'no'. Today 50-50. He was a little bit better this morning. But 50-50.”
Should Kante miss out his absence would add to a growing injury crisis in midfield, with Ruben Loftus-Cheek and Callum Hudson-Odoi both missing with long-term injuries.
“We are in trouble with the midfielders," Sarri admitted. "At the moment we have only three midfielders for three positions, so we are in trouble.
"For us, N'Golo is really very important. He is the only defensive midfielder that we have, so for us he is really very important.
"We are trying to recover him. We will try tomorrow morning. I hope to recover him because I know very well that, without N'Golo, for us it's a problem.”
Sarri's future at Chelsea is in doubt after just one season, but the Italian defended his record in a campaign that saw his side finish third in the Premier League and reach the Europa League final as well as the Carabao Cup final.
“We did a wonderful season because, in the last season, Chelsea weren't in the Champions League," Sarri said. "Now we are in the Champions League.
"We played a final in a competition in which we played against Liverpool and against Tottenham, and qualified. Against the two finalists in the Champions League. Then we lost the final on penalties to Manchester City, the best team in Europe at the moment.
"And now we play the final in the Europa League. We played a very good season. Of course, if now we can win the final, the season will become wonderful.”