The final four places in the quarter-finals are up for grabs this week, although unlike United who remain hopeful of salvation, Zenit St Petersburg and Schalke travel to Borussia Dortmund and Real Madrid respectively facing mission impossible.
Dortmund won the first leg 4-2 in Russia while Spanish league leaders Real ran riot in Germany, winning 6-1.
Premier League Chelsea still have plenty of work to do, however, as they welcome back former striker Didier Drogba to Stamford Bridge hoping the Ivorian does not help Galatasaray continue the English exodus from the competition after last 16 defeats for Arsenal and Manchester City.
Jose Mourinho’s side were held to a 1-1 draw in Istanbul in the first leg and will start as favourites to finish the job on Tuesday.
With a top-four finish in the Premier League now looking a remote possibility after a 3-0 home defeat by Liverpool on Sunday, United’s only realistic hope of competing alongside Europe’s elite next season would appear to be by somehow winning the competition for a fourth time in May.
Judging by the current malaise at Old Trafford that would seem a fanciful notion, but under-pressure manager David Moyes said his side would fight tooth and nail to keep the season alive.
“The players are well aware of what it means on Wednesday and what we have got to do,” Moyes said.
“We’ve got something to go for so hopefully we can do that.”
United have a 100 percent record at home against Greek opposition while Olympiakos have lost each of the 11 matches they have played on English soil.
Worryingly for United they have only on one occasion managed to overturn a first-leg deficit in the Champions League, crushing Roma 7-1 in 2007 after losing the first leg 2-1.
Olympiakos will also be buoyed by a 2-0 win over Panathinaikos on Saturday that secured a 41st Greek title.
“We know we are very close to achieving something great,” Olympiakos’s Costa Rica forward Joel Campbell, a loanee from Arsenal who scored in the first leg, said of Wednesday’s return.
“Performing at Old Trafford is extremely important. I believe it is every player’s dream.”
Chelsea will need to clear their heads quickly after Saturday’s meltdown at Aston Villa where they lost 1-0, had midfielders Willian and Ramires red-carded and manager Jose Mourinho sent from the dugout.
In Drogba, Chelsea know the Turkish club have a player more than capable of capitalising on any hangover from the Villa debacle, although he has mixed feelings about the task ahead.
“First of all I’m happy to play against my ex-club, against my friends,” he told UEFA广西桑拿,. “But at the same time it is a very special moment because I do not know what my reaction will be. You know that I spent eight years at Chelsea, so I really don’t know, I am quite apprehensive about it.”
(Reporting by Martyn Herman; editing by Justin Palmer)