"We have already lost Ney", Tuchel added.
The Brazil captain has been ruled out until at least April with a foot injury and Cavani failed to appear for the second half of PSG's 1-0 victory over Girondins on Saturday. But they will still feel the absence of Neymar and Cavani - if the latter can't play.
PSG faces United in the return leg of their last-16 match on March 6, with some French media reporting Cavani will be out for one month.
"My feeling is that it's going to be very hard for him to play".
And PSG coach Tuchel told TF1's Telefoot on Sunday morning: "There is no good news this morning". In any case, we must wait.
United have been handed a huge boost ahead of their crunch European tie with PSG, with talisman Edinson Cavani set to sit out through injury.
Marco Verratti is also a doubt, the midfielder managing only 59 minutes against Bordeaux after recovering from an ankle injury. "But we're ready for Manchester and I have faith in my players". We are no longer looking at Plan B, but Plan D!
PSG are 13 points clear at the top of Ligue 1 but their win over Bordeaux came after their toughest week of the season. That match is just two days away, but it will be important to see if he is at training leading up to the game.
However, Tuchel says the Italy global is eager to play a part. Verratti played nearly an hour before being substituted by Leandro Paredes.
Mid-table Bordeaux slumped to a fourth straight loss between league and cup, although they almost equalised on the hour when Francois Kamano's shot from 20 yards was superbly saved by Gianluigi Buffon.