The Premier League holders welcome the Greek club - who won their fourth straight league title on Saturday - to Old Trafford on Wednesday for the second leg of a last 16 tie, desperate to overturn a 2-0 deficit from the return match.
United manager David Moyes has come increasing pressure at Old Trafford following a disappointing maiden campaign, and his misery was compounded by a hugely disappointing 3-0 loss at home to rivals Liverpool on Sunday.
A brace of penalties from Steven Gerrard helped to inflict a fifth home league defeat of the campaign on United, but perhaps more worrying for Moyes was the way his side were outplayed by Brendan Rodgers' men.
The Champions League can now provide some solace for Moyes, whose side trails Chelsea by 18 points in the English top flight, with Europe's premier competition providing United's last chance of silverware this season.
To progress to the quarter-finals United will have to erase Olympiacos' two-goal cushion, gained through strikes from Alejandro Dominguez and on-loan Arsenal forward Joel Campbell.
Moyes has vowed 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 said. "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."
Olympiacos 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 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 the hosts show following the Liverpool defeat.
United head into the match without Jonny Evans (calf), while Michael Olaitan has not played for Olympiacos 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.
