The Red Devils must overturn a two-goal deficit to see off the Greek champions, advance to the last eight of the competition and ease the pressure on their manager
The Premier League holders welcome the Greek club - who secured their fourth straight league title on Saturday - for the second leg of their last-16 tie, desperate to overturn a 2-0 deficit.
United manager David Moyes has come increasing pressure at Old Trafford following a disappointing maiden campaign and he spent Monday locked in crisis talks with his backroom team after Sunday's 3-0 humiliation at the hands of bitter rivals Liverpool.
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With United trailing Premier League leaders Chelsea by 18 points, the Champions League provides an unlikely last chance of silverware this season.
To progress to the quarter-finals, though, the Red Devils would have to erase Olympiakos's two-goal cushion, gained through strikes from Alejandro Dominguez and on-loan Arsenal forward Joel Campbell.
Moyes has vowed that United will turn the tie on its head, acknowledging the need to start Wednesday's game well.
"We have to go for the throat to get the win," he told reporters. "We won't be gung-ho but we will certainly go with a mindset to overhaul the deficit as quickly as we can.
"We won't be reckless as we could find ourselves with a bigger mountain to climb, but we can be forceful. We have to be if we're to keep ourselves in the Champions League."
Olympiakos have lost on all of their previous 11 visits to England but travel to Old Trafford on the back of lifting a 41st Greek title with five matches to spare, thanks to a 2-0 victory over Panthrakikos.
Furthermore, Michel's men showed that they are more than capable of competing against United in the first leg at the Karaiskakis Stadium and they will look to pounce on any mental fragility that the hosts show following the Liverpool defeat.
United head into the match without Jonny Evans (calf), while Michael Olaitan has not played for Olympiakos since collapsing against Panathinaikos at the beginning of March. Ivan Marcano (groin) and Javier Saviola (quadriceps) are doubts for the visitors, while Dominguez, Kostas Manolas and Diego Fuster are all one booking away from a suspension that would rule them out of a quarter-final tie.