But the reality for manager David Moyes and his stuttering team is that present form, rather than past successes, will have a far bigger influence at Old Trafford. (Agencies)
United's unimpressive season reached a new low on Sunday when they were crushed 3-0 at home by bitter rivals Liverpool, a result that left last season's champions seventh in the Premier League with just a remote possibility of a top-four finish.
Their only realistic hope of competing alongside Europe's elite next season would now appear to be by somehow winning the competition for a fourth time in May, starting by knocking Olympiakos out on Wednesday.
"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," he said.
Misfiring United, who last failed to qualify for the Champions League 18 years ago, have no guarantees at all of achieving their aim against the Greeks who have just won their domestic title for the fourth successive season, the 16th time in 18 campaigns they have ended as champions and the 41st in all.
Their head-to-head record, and the Greek side's woeful record on the road against English clubs, does offer hope.
Until Olympiakos triumphed in Athens on Feb. 25, United had won all four of the previous matches between the clubs.
They have also won all five matches they have played against Greek clubs at home while Olympiakos have lost all 11 of the matches they have played in England.
That sorry sequence began with a 4-0 loss at West Ham United in the old European Cup Winners' Cup in 1965 and has continued since with subsequent defeats at Tottenham Hotspur, Liverpool (twice), Newcastle United, Chelsea, Manchester United (twice) and Arsenal (three times).
But they arrive at Old Trafford buoyed by a comprehensive title victory, even if Sunday's 2-0 win over Panthrakikos was achieved behind closed doors.
But the reality for manager David Moyes and his stuttering team is that present form, rather than past successes, will have a far bigger influence at Old Trafford.