The midfielder went off with a hamstring injury in the ninth minute of Chelsea's Premier League clash against Watford on Sunday.
He is now set to miss the Blues' European semi-final second leg against Eintracht Frankfurt but is targeting a potential return on May 29 should Chelsea progress on Thursday night.
Sarri previously took responsibility for the 28-year-old's injury, but Kante refused to blame his manager.
Speaking at a news conference ahead of the semi-final, Sarri said: “Kante had a problem with his hamstring, not really a very serious one but he needs to rest for a couple of weeks. So we can try to recover him only in case we reach the final.”
Probed further on whether the France international was likely to overcome the injury in time for the final, Sarri added: “We can try. I am not sure, but we can try.”
But, with the winner of the Europa League also being awarded 2019-20 Champions League qualification, Sarri insists his side's league position has not affected their motivation ahead of their semi-final.
"We reached the target of the club, so we are really very happy with this.
"Now we have to play in another competition and the target is to reach the final – the first target – and the final target will be to win the competition. Our feeling is that we deserve to win a trophy, so it's a very important match, of course.
"We have to play to win, without managing the results. That's too dangerous (to do). It's not easy because we play a very dangerous team, as we saw in the first leg.
"They are very dynamic and aggressive in the defensive phase, and dangerous in the offensive phase especially when they find spaces on the counter-attack. So it's a dangerous match."
If they progress, Chelsea will play either Arsenal or Valencia in the final.