The first leg is to be held at Old Trafford before the trip to Germany to face the holders at the Allianz Arena.
The runaway leaders of the Bundesliga knocked Arsenal out in the previous round and also topped Manchester City's qualifying group. The two sides last met in 2010 when Bayern triumphed on away goals after Rafael was sent off in the second leg in Manchester. Of course, there were three matches between the clubs in 1998/99 with the Reds winning the final in dramatic circumstances to complete the Treble.
All eight group winners progressed from the previous round to ensure a high quality line-up with United roaring back against Olympiacos during the memorable clash in midweek to overturn a two-goal deficit from the first leg in Greece.
The ties will be played on Tuesday 1 April and Wednesday 9 April as the road to Lisbon on 24 May continues.