Fernando Torres will come up against his old side Atletico Madrid after Liverpool were paired with the Spanish side, Marseille and PSV Eindhoven in Group D.
Arsenal will be confident of progressing after being drawn against FC Porto, Fenerbahce and Dynamo Kiev in Group G.
United and Celtic locked horns in the group stages two years ago, with both sides claiming one win apiece in the two meetings, and it will be Gordon Strachan who pits his wits against former boss Sir Alex Ferguson again.
Bruce Rioch's Aalborg and Spanish side Villarreal make up the rest of Group E.
Elsewhere, Group H looks the toughest one to call with nine-times winners Real Madrid, returning Italians Juventus, Uefa Cup holders Zenit St Petersburg and Belarus champions Bate Borisov making up the group.
Barcelona have been handed a favourable draw in Group C, as they face Sporting Lisbon, Basel and Shakhtar Donetsk.
Rome's Stadio Olimpico will stage the final on 27th May 2009.
The first set of matches are due to be played on 16/17 September.
Zenit St Petersburg