The England captain has enjoyed a stunning start to life in Germany after leaving Tottenham in August.
Kane has already scored 22 goals in just 19 games for the Bavarian giants while laying on a further seven assists, breaking Bundesliga records.
Bayern have already won Group A and are safely into the next round but Tuchel will not be resting his star man after his team were thrashed 5-1 by Eintracht Frankfurt on Saturday.
United, who were strongly linked with Kane prior to his move to Germany, are up against it after a calamitous European campaign.
Erik ten Hag’s side have won only one of their five group games, conceding 14 times in the process and must rely on other results to progress.
Even if they were to beat Bayern on Tuesday night, the Manchester giants would still need Copenhagen and Galatasaray to draw in the group’s other game.
"I think every fan wishes they had Harry in their team, that's why we are very proud that we managed to sign him,” said Tuchel.
“He is a big personality, a big player and a role model. He scores a lot of goals and will be happy to be here and to play tomorrow."
Jamal Musiala, however, is carrying a slight knock and Tuchel has confirmed the midfielder will not be able to play a full 90 minutes.
"Jamal is still not able to play for the full 90 minutes,” added the Bayern boss.
“He will either start or he will come on and get a feel for the game. I still haven't decided."