Rated at no better than 18/1 ahead of the quarter-final draw, United are only seventh in the Premier League table.
The lowest league position of any of the other seven teams left in the competition this season is third - which is Barcelona's spot in Spain behind Real and Atletico Madrid who are first and second respectively.
But Rooney is not down-hearted, he said: "I think in cup football anything can happen.
"We're in the quarter-final so you never know what can happen from there.
"You look at the three Spanish teams left in the competition, they're all good teams.
"Chelsea are probably playing the best football this season. I know they lost at Aston Villa but they're playing some good football and obviously you've got Bayern Munich.
"PSG are playing well. It's a talented group of teams so whoever we get it will be tough."
The 28-year-old England striker also said that the players knew they had performed badly against Liverpool last week and were desperate to hit back against Olympiakos in midweek - when they won 3-0 to qualify for the last eight.
He told The Mirror: "I'm not going to confirm the details of what happened but obviously we talk.
"We talk after every game, whether we win, lose or draw but we knew as a team what went wrong on Sunday.
"We didn't need anyone to tell us and we came out and delivered a big performance against Olympiakos."
As for their campaign so far, he added: "Our performances this season haven't been good enough and we owed the manager a big performance.
"We know as players we're better than what we've done this season. As a group we have to show that and put it right.
"I think it was always going to be tough when Sir Alex Ferguson left. It was obviously a massive change but we didn't expect it to be as tough as it has been.
"But we have to put that right. We have to keep working, keep believing in ourselves and hopefully it'll get better."
The draw will be made at UEFA's Nyon headquarters at 11am UK time, with the two-legged ties to be played on 1/2 and 8/9 April.
Benfica's Estadio da Luz in Lisbon will stage the final on 24 May.
It is the first time in the Champions League era that all eight group winners have made it into the quarter-finals.
And for the second season running, Spain provides three of the last eight, Germany and England supplying two each and France just one in the shape of Laurent Blanc's PSG.
Champions League quarter-finalists:
Follow the Champions League and Europa League quarter-final draws on skysports.com, the Sky Sports apps or on Sky Sports News from 11am on Friday.