The Uruguay worldwide was forced off just moments after scoring a 42nd-minute penalty in Saturday evening's 1-0 win over Bordeaux in Ligue 1.
PSG visit Old Trafford on Tuesday for the first leg of their encounter in the round-of-16, the stage at which the French champions went out in the last two seasons.
"No, I don't have good news for you", Tuchel told Canal +. "He had exams yesterday and he still has exams here today in our training centre". My feeling is that it will be very hard for him to feature in Manchester. In any case, we must wait. The club will communicate on this a bit later. In my opinion, the news will not be very very good. "We always hope but the first exams are not good". "In matches like these, decisive Champions League games, you absolutely need your key men as they are experienced in handling pressure in matches like this one".
Tuchel said there was good news for another of his key players, midfielder Marco Verratti who started against Bordeaux after three weeks out with an ankle problem.
"On Tuesday, a very important game is waiting for us", he said, per Goal.
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However, with the Portuguese's sacking, United have been on the uptrend under Ole Gunnar Solskjaer and they are now unbeaten in 11 successive games which includes 10 wins.
And Mbappe's highlights from the second-half look promising for United, because without Neymar and Cavani, he was forced to drop deep a lot.
It's a potentially big blow for the French team but also a boost for Ole Gunnar Solskjaer's Manchester United.
And speaking after the game, Tuchel said: "If he [Cavani] comes off, obviously I am anxious". Verratti played nearly an hour before being substituted by Leandro Paredes.
PSG face rejuvenated Man United side who are yet to lose since the arrival of Solskjaer in December 2018.