The struggling Red Devils were boosted by a 2-0 victory over Crystal Palace at the weekend but are going up against a side unbeaten in the Super League for a year
It was always going to be a tough season for the three-times champions of Europe, with David Moyes facing the unenviable task of replacing Sir Alex Ferguson at the helm.
United's Premier League form may be inconsistent, but Moyes' men have looked convincing in the Champions League, topping Group A, remaining unbeaten and conceding just three goals in six games.
Last Friday's news that striker Wayne Rooney had signed a new deal until 2019 was well received by the club's supporters and the England striker scored 24 hours later in a 2-0 victory at Crystal Palace.
Just as encouraging for Moyes is the return of Robin van Persie after a campaign that has been blighted by injury. The Dutchman has still managed to score 14 goals in all competitions this term, with four coming in his last five league games.
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January signing Juan Mata is ineligible, having played for Chelsea earlier in the competition. In more positive news, Darren Fletcher has been added to United's Champions League squad.
United face an Olympiakos side that are coasting the Super League in Greece. Michel's men are unbeaten in the league since February last year and have this season amassed an astonishing goal difference of plus 69, conceding just nine goals.
Olympiakos made it to the last 16 in dramatic circumstances, finishing second in Group C behind Paris Saint-Germain to progress at the expense of Benfica thanks to a superior head-to-head record.
Michel's team could not be going into Tuesday's first leg in better form after demolishing OFI Crete 4-0 at the weekend, a game that included a hat-trick for Serbian striker Marko Scepovic. Like Mata, though, he is ineligible.
But the victory came at a price. Scepovic got his chance because of a thigh injury to forward Javier Saviola, who will now miss the match with United.
January additions Hernan Perez and Ivan Marcano are both available for Tuesday's clash, though, while Nelson Valdez also joined last month, but an ankle injury means he is a doubt.
The omens are not good for the Greek side. In four Champions League meetings with Manchester United, Olympiakos have been defeated four times, scoring just twice.