Bottom side United, on four points, can still make the last 16 if they beat visiting Bayern and Galatasaray draw at second-placed FC Copenhagen, with both of those teams on five points.
The Bavarians will look to perk up their confidence at Old Trafford after seeing their unbeaten Bundesliga run this season end as they were hammered 5-1 by Eintracht on Saturday.
Bayern secured first place in Group A with 13 points last time out but a 0-0 draw at home to Copenhagen snapped their 17-game winning run in the competition's group stage.
"I understand that some people thought that against Copenhagen it looked like we weren't throwing everything into it," Tuchel said.
"But when you sign for Bayern or (Manchester) United, you sign to give 100 percent every day. When you wear the Bayern Munich jersey, you behave like champions, there's no other way. We have high expectations, even if we're always under pressure.
"United will give everything tomorrow to get through," added Tuchel. "But we expect a top performance from us. I hope we can match United's enthusiasm and energy, which I'm sure they'll bring to the game."
The German said Bundesliga top scorer Harry Kane will play as he returns to England after his move from Tottenham Hotspur in August for a reported 100 million euros ($107.62 million).
"(Harry) scores a lot of goals and will be very happy to play here tomorrow," Tuchel said. "It's a great story that we were able to bring the England captain to Germany."
