The Red Devils won the 2008 European title and after signing a five-and-a-half-year deal with the club, Rooney is eager to help lead the team more glory on club football's biggest stage.
"You always want to win it," said Rooney ahead of Tuesday night's Champions League Round of 16 first leg with Olympiakos in Athens.
"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."
United meet the Greek champions at the Karaiskakis Stadium in the first leg before hosting the Piraeus giants at Old Trafford in the return bout on March 19.
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