The clubs have enjoyed contrasting fortunes domestically this season, with Bayern having already retained their Bundesliga title while English champions United languish sixth in the Premier League.
All-conquering UEFA Champions League holders Bayern were expected to sweep David Moyes' team aside in the first leg of their quarter-final at Old Trafford last Tuesday, but a spirited display from United saw them claim a 1-1 draw to take to the Allianz Arena this week.
United have endured a tricky first campaign under Moyes, who replaced the legendary Alex Ferguson last July, with the club now mathematically certain to relinquish their Premier League title as they sit 17 points adrift of leaders Liverpool with five games to play.
They also look likely to miss out on qualification for the Champions League for the first time since 1995-96, as they are seven points behind fourth-placed Arsenal.
Bayern, meanwhile, have continued to flourish under Pep Guardiola's guidance, with the Bavarians wrapping up the German title with seven matches to spare and remaining on course to retain both their Champions League and DFB-Pokal crowns.
Bastian Schweinsteiger's away goal last week - which levelled Nemanja Vidic's opener - puts them in the driving seat to reach the semi-finals, although they will be without the Germany international midfielder through suspension after he was dismissed for a second bookable offence late on at Old Trafford.
However, United left-back Patrice Evra, who returns after missing the first leg due to a one-match ban, believes his side can emulate Chelsea's 2011-12 season, when the London club finished sixth in the Premier League but won the Champions League - beating Bayern in the final.
"It was funny because all season reminded me of the Chelsea season they won the Champions League when they were not playing well in the league," Evra said.
"I am not saying we are going to do the same but sometimes you have to be positive, so why not?
"Of course it is unusual for us to say we can save our season in one game. Now we must make sure the fans will be proud for the second leg against Bayern."
Bayern head into the fixture with the unfamiliar feeling of losing, as a 1-0 setback at Augsburg on Saturday ended the club's record 53-match unbeaten run in the Bundesliga.
Guardiola shrugged off the defeat, but described the second leg with United as a "life or death match".
By contrast, United were dominant in a 4-0 win at Newcastle United on Saturday, though Juan Mata, who scored twice at St James' Park, is ineligible.
Striker Robin van Persie also remains absent with a knee injury, while Wayne Rooney could also miss out due to a toe problem.
As well as Schweinsteiger, Bayern are also without Javi Martinez through suspension, while Thiago Alcantara is sidelined with a knee problem and Xherdan Shaqiri (thigh) is doubtful.
