David Moyes's men were drawn the reigning champions in the final eight, with the first leg in April being held at Old Trafford.
"It's an exciting tie," BBC Sport quotes Alexander as saying. "Bayern are a fantastic side, but we have to take heart from our performance the other night against Olympiacos.
"Our staff are very thorough and will have done their homework and will be prepared for Bayern. If we can keep them quiet in the first leg and get an advantage then we're more than capable of stealing an away goal."
United's fellow Premier League side Chelsea were drawn Ligue 1 champions Paris Saint-Germain.