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."
For all the talk of promise under Moyes, Rooney did accept that he and his team-mates have not performed well enough for the man who was hand-picked for the role by Sir Alex Ferguson last year.
"As a group of players we have to take responsibility for our league position," Rooney added.
"We know we're better than that and we haven't performed as well as we can do.
"We know that and it hurts. Now it's important we finish the season strongly and take some momentum into next year, but more importantly get into fourth spot and do well in the Champions League."
One of the reasons why United have suffered this season is because Moyes has been deprived of his first-choice strike partnership for much of the year.
Indeed, throughout their time at Old Trafford, United have only lost two of the 36 games they have started together.
Rooney admits it has been a frustrating period for him in that respect.
"Robin is a fantastic player," Rooney said.
"He is one of the best goal scorers in world football.
"We've got a good record when we've played together but unfortunately we have had injuries at similar times but hopefully we can stay fit and help us win games.
"When we're fit, we'll score goals, but we've also got other players who can come in and score goals too."
Olympiacos are unbeaten at the top of the Greek Super League this season, but they had not reached the last 16 of the Champions League since 2010.
With top scorer Javier Saviola out through injury, United are favourites to win the first leg in the Greek capital, but Moyes says he is not taking the match lightly.
"It will be far from easy," the United boss said.
"Olympiacos came through a difficult group with Benfica, Paris St Germain (and Anderlecht).
"They have a great home record so it will be a difficult night."
Moyes confirmed that injured defenders Phil Jones and Jonny Evans have not travelled with the squad.
Midfielder Nani is also unavailable because of a hamstring injury, but Rafael and Danny Welbeck are back following their respective head and knee problems.