Cavani scored the only goal of the game from the spot in PSG's win over Bordeaux on Saturday, but he was unable to finish the match and limped off soon after finding the net, reportedly with a thigh strain.
The Uruguay international was one of few PSG stars to start the match, as Tuchel kept the likes of Leandro Paredes and Kylian Mbappe in reserve ahead of the last-16 first leg at Old Trafford.
PSG are already without Neymar for the match and Tuchel accepts Cavani may have to miss out as well, dealing the Ligue 1 champions a major blow ahead of facing a United side who have won 10 out of a possible 11 matches under interim manager Ole Gunnar Solskjaer.
"There are lots of plan Bs now," Tuchel told reporters. "Without Ney [Neymar], maybe without Marco, maybe without Edi [Cavani], now we need a plan D.
"I can't think about so many different plans in advance. We have to analyse Manchester United, we have to stay calm and confident.
"Normally, my opinion is definitely clear: for a game against Manchester United, for a game against Liverpool or even against Red Star Belgrade, you need your key players with confidence, experience, quality, who are used to playing that kind of game, are used to playing big games full of pressure, who are used to managing the pressure.
"But, if two or three key players are not here, it's our duty to find solutions. It's very difficult if we play with our best team, it's a big challenge. If we are missing lots of key players, it's an even
Speaking on Sunday morning, Tuchel added to TF1: “We don't have good news for Edi. My feeling is that it will be very difficult for him to play.
“The club will wait a little longer, but in my
Verratti played for an hour on Saturday after three weeks out with an ankle injury, and Tuchel admitted he might have to risk the Italian due to their injury problems.
"Obviously, we are very happy Marco is back with us," Tuchel added. "He brings quality, as we could see today. After he left the pitch, it was more difficult for us to control the game.
"Normally, it's very difficult to play so soon when you have been injured as Marco has. It was his first game since his injury.
"He played 60 minutes, I don't know if it's possible for him to play again at Old Trafford against Manchester United only three days later.
"But, in our situation, it's maybe necessary to try to make him play. We have to decide tomorrow [Sunday] about that. We have to wait for Marco's opinion.
"But, obviously I already know Marco's opinion. If I ask him if he can play [he will want to play] … But we have to wait for the doctor's opinion to see if it's possible or not."