David Moyes' men were pitted against the reigning champions and tournament favourites in Friday's draw, with the first leg to be played at Old Trafford on April 1 before the return game in Munich eight days later.
It is a repeat of the 1999 final, when United staged an incredible comeback in the final moments to snatch a dramatic 2-1 victory at Camp Nou.
The two sides last met four years ago, also in the quarter-finals, with Bayern progressing on away goals.
The German side have been in astonishing form this season and look destined to claim the Bundesliga crown once again, but Alexander called on United to use their stirring comeback against Olympiacos as a source of inspiration.
"It's an exciting tie," he told UEFA.com.
"Bayern are a fantastic side, but we have to take heart from our performance the other night against Olympiacos."
The Premier League champions beat Olympiacos 3-0 on home soil on Wednesday to progress 3-2 on aggregate.
