United return to Champions League action on Tuesday when they play the first leg of their last-16 clash against Olympiacos in Greece.
As they are 11 points behind fourth-placed Liverpool, winning the Champions League could end up being the easiest route back into the competition next year.
With Barcelona, Bayern Munich and Real Madrid all expected to feature in the quarter-finals, United are 25-1 shots to win the competition with some bookmakers.
But one of the reasons Rooney signed a new five-and-a-half year deal with United was because he thinks he can win more winner's medals with the club and he thinks this could be United's year.
"We've certainly got the quality in the team to go really far so hopefully we can do that," the United striker said.
"We've been excellent in the Champions League this year and hopefully we can take that into the game tomorrow night."
Rooney looked destined to leave United last summer, but he has buried the hatchet with manager David Moyes and is sure the Scot is the right man to bring the glory days back to Old Trafford.
Rooney may have been at United for 10 years now, but his appetite for glory has not diminished.
"You always want to win it," said Rooney, who was part of the United team that beat Chelsea in the final six years ago.
"One is never enough, especially at this club.
"We need to keep trying to get into finals.
"The feeling you get when you win a trophy is incredible so you don't want to stop at one. If we can go to final it'd be great for us. It would be an opportunity to win another trophy, so hopefully we can do that.
"I grew up all my life wanting to win trophies. That's the main aim. That's what you'll be judged on when you finish your career."
Midfielder Nani is also unavailable because of a hamstring injury, but Rafael and Danny Welbeck are back following their respective head and knee problems.
Olympiacos manager Michel believes United could buckle under pressure when the two sides meet in the white-hot cauldron of the Karaiskakis Stadium.
Athough his side look weak opponents on paper, the 28,000-strong home crowd will do everything they can to make United's well-paid stars uncomfortable.
Michel believes the importance of the game could have a bearing on United's performance.
"We know there's lots at stake for Manchester United in this match," the Spaniard said.
"We know Manchester United are not allowed to make any mistakes due to their position in the Premier League and we have to say probably this kind of situation may weigh too much on their players' shoulders.
"It could be an incentive to them or it could be a burden on their shoulders.
"People say it'll be a very demanding tie and that's true. They are favourites, but nothing says we can't beat Manchester United."
Michel's preparations for Tuesday's game took a hit on Saturday, though, when top scorer Javier Saviola was ruled out with a thigh injury.
Having sold Kostas Mitroglou to Fulham in January, and with fellow striker Marko Scepovic cup-tied, Olympiacos only have one registered frontman who is fully fit in 21-year-old Michael Olaitan.