Seven clubs from five different countries could be paired with United in Friday's UEFA Champions League draw at 11:00 GMT.
You can follow events in Nyon, Switzerland, in Ben Hibbs' Live Blog from 10:00 GMT.
Here we take a look at the possible opponents, with their Betfair odds for winning the competition in brackets. Odds subject to change - see manutd.com/bet for the latest info.
Bayern Munich (23/1) secured their last-16 place with a magnificent 4-1 away win over rivals Juventus. The 2001 winners have some fantastic attacking options - with Luca Toni, Mario Gomes, Miroslav Klose and Ivica Olic all competing for places - and even their goalkeeper Hans Jorg Butt has scored this season, from the spot in the Juve game.
Internazionale (13/1) were paired with United at this stage last year, with the Reds securing a 2-0 aggregate victory. Jose Mourinho’s side came close to not qualifying but a last-day win over Rubin Kazan put them through with a mere nine points.
Lyon (79/1) won their first three group games, including the pivotal victory at Anfield where Cesar Delgado scored a last-minute winner. United beat Lyon in a close last-16 encounter (1-1, 1-0) in the triumphant 2007/08 campaign.
Milan's (26/1) rich history includes seven European Cups, two in this decade, but they needed a last-day draw at FC Zurich - and Real Madrid's win at Marseille - to go through. Filippo Inzaghi is still potent, netting two goals in the group stage.
Olympiakos' (219/1) home record has been the key to their passage into the next stage; the Greeks won all three games at the Georgios Karaiskakis Stadium, and qualified with the last one against an understrength Arsenal side.