Rooney, who was reportedly wanted by Chelsea in the summer, ended speculation regarding his future last week when he put pen to paper.
The England forward is committed to bringing the glory days back to Old Trafford and he hopes this will be the year he wins his second Champions League with United.
Rooney was in the team which conquered Europe by beating the Stamford Bridge club in Moscow in 2008.
"You always want to win it," said Rooney who was sitting alongside manager David Moyes at a press conference in Piraeus ahead of United's last-16 first-leg clash with Olympiakos on Tuesday night.
"One is never enough, especially at this club. You have to keep trying to get into the final when you are at this club.
"The feeling you get when you win it is incredible, so there is no way that you want to stop.
"If we can go to the final then it would be great for us. It would be an opportunity to win another trophy, and hopefully we can do that."
Although Olympiakos are one of the weaker teams in the competition, United are still outsiders to reach the final in Lisbon on May 24.
David Moyes' team sit 11 points off fourth place in the Premier League with 11 games to go, but Rooney still thinks it would be foolish to write off United's chances of reigning supreme in Europe this term.
"The year Chelsea won it, they nearly went out of the competition about three times," the United striker said.
"We've been excellent in the Champions League this year and hopefully we can take that into the game (on Tuesday night) and that will help us get the result. We've got quality in the team to go far, so hopefully we can do that."
Olympiakos - who are without top scorer Javier Saviola through injury - are unbeaten at the top of the Greek Super League this season, and have lost just twice in the last four years at home in the domestic league.
They have lost all four previous meetings with United but David Moyes is not expecting a comfortable night at the Karaiskakis Stadium in the last four years.
"It will be far from easy," the United boss said.
"Olympiakos came through a difficult group with Benfica, Paris Saint-Germain (and Anderlecht). They have a great home record so it will be a difficult night."