The Greek hosts have so far lost all four of the previous clashes between the two clubs, scoring just twice in the process.
Ahead of the last-16 first-leg tie in Athens, Sports Mole has looked back over the quartet of group encounters which have ended with United prospering.
1. Olympiacos 0-2 Man United, October 2001
Just a few days after he had inspired England to a late victory over the Greece national side with a stoppage-time free kick, David Beckham went on to haunt the European nation's best club side. After a first half without a goal, the right-winger broke the deadlock when he ghosted in to convert Ryan Giggs's cross in the 66th minute. Andy Cole then made sure of the outcome in the closing stages as he scored from close range following an exchange with Ruud van Nistelrooy.
2. Man United 3-0 Olympiacos, October 2001
Having lost twice to Deportivo La Coruna, United had a battle on their hand to progress as group winners. It appeared that Sir Alex Ferguson's side were also going to be frustrated by Olympiacos at Old Trafford, especially after Van Nistelrooy had seen a second-half penalty saved. However, three late goals from Ole Gunnar Solskjaer, Giggs and Van Nistelrooy sealed the victory for the hosts, which in turn saw them qualify for the second group stage.
3. Man United 4-0 Olympiacos, October 2002
A season later, Olympiacos arrived in Manchester having failed to win any of their previous 17 Champions League away matches, and from the moment that Giggs opened the scoring for United in the 19th minute, that run always looked likely to be extended. Argentine midfielder Juan Sebastian Veron soon doubled the home team's advantage with a deft chip, before goals after the restart from Giggs and Solskjaer put some gloss on the result.
4. Olympiacos 2-3 Man United, October 2002
It was only the fourth game of the group stage, but United's win saw them seal their place in the second group phase. A goal either side of the break from Laurent Blanc and Veron put the away team in command, but soon after Olympiacos achieved something that they hadn't managed before - score against United. Lambos Choutos and Predrag Djordjevic drew the hosts level with goals in quick succession, but six minutes from the end Dimitrios Eleftheropoulos failed to hold Paul Scholes's shot from the edge of the area and the ball flew into the top corner of the net.