Sunday's 3-0 loss to Liverpool left David Moyes's side 12 points below the top four in the Premier League and, having already gone out of both domestic cups, the Champions League represents a last chance of salvation.
Notions of the club qualifying for next season's Champions League by winning the current tournament appear fanciful, but elimination in the last 16 on Wednesday would suck all intrigue from their campaign.
Succeed, and United will take their place alongside Europe's most glamorous sides in the quarter-finals, three years after last reaching the last eight en route to defeat by Barcelona in the 2011 final.
Fail, and the unwanted consolation of a Europa League place will be all that is left to play for; a fraught summer of soul-searching all there is to look forward to.
United were synonymous with stirring comebacks under Moyes's predecessor, Alex Ferguson, but they require a vast improvement on the insipid showing produced against Liverpool.
Worryingly for both United's supporters and the club's hierarchy, the team's performances appear to be getting worse, despite strikers Wayne Rooney and Robin van Persie both now operating at full capacity.
They offered disconcertingly little resistance in the first-leg loss to Olympiakos in Piraeus on February 25, but goalkeeper David de Gea has promised an improved showing in the return fixture.
"We know we didn't play a good match in Greece
They were better than us and they won," the Spaniard told the UEFA website.
"But now there is the return leg at Old Trafford and I think that, with our fans behind us, we have to go onto the pitch and fight and attack from the first minute.
"We will give everything we have and play a lot better than we did there."
- Maradona vanquished in 1984 -
United have recovered a first-leg deficit only once in the Champions League era, atoning for a 2-1 loss to Roma in the quarter-finals of the 2006-07 tournament with a stunning 7-1 victory at Old Trafford.
They twice overturned 2-0 scorelines in the now defunct European Cup Winners' Cup, however, beating Tottenham Hotspur 4-1 in 1964 and storming back to beat Diego Maradona's Barcelona 3-0 in the quarter-finals in 1984.
Moyes reported no fresh injuries after the defeat by Liverpool, although Spanish midfielder Juan Mata will drop out of the squad as he is cup-tied.
"The players are capable of turning it around," said Moyes, whose side won all three of their home matches in the group phase.
"It's something to go for, it's another game, and we'll do everything possible to make that work."
Olympiakos's first-leg success unexpectedly proved the catalyst for a downturn in their domestic fortunes, as they slumped to consecutive defeats -- their first of the season -- against Panathinaikos and PAOK.
They returned to winning ways on Saturday, however, beating Panthrakikos 2-0 at the Karaiskakis Stadium to secure a 41st Greek league title -- their fourth in succession.
Manager Michel rested several first-team players with a view to Wednesday's game, but experienced forward Javier Saviola is a doubt after playing only a limited role in Monday's training session.
Nigerian forward Michael Olaitan and Greek defender Dimitris Siovas have been ruled out due to injury, but Spanish centre-back Ivan Marcano is in contention after a calf problem.
"We know very well what the team is going to face
We know how difficult it will be," said Michel, who won six league titles and two UEFA Cups as a midfielder with Real Madrid during his playing career.
"Two-nil is not a significant advantage and if we want to advance, we will have to go there and score a goal."
Olympiakos, who have lost on all of their 11 previous visits to England, are bidding to reach the quarter-finals for the first time since 1999.
Source : AFP
Source: AFP