Roberto Mancini's side was dumped out of Europe altogether following a 1-0 defeat to Borussia Dortmund on Tuesday, while speculation has grown over the Italian's future at the Etihad Stadium.
City currently trails United by three points and a win for Sir Alex Ferguson's men will put even further daylight between the two clubs at the top of the Premier League.
"City are out of the Champions League and are having a bit of a tough time - I think everyone can see that behind the scenes. If we win, we can put more pressure on them. If we get three points there, it will be massive for us." Rooney told reporters.
"Obviously, it is a massive game, probably up there with Liverpool. The two of them. There is a big rivalry, the two of us are fighting for that number-one spot. We're trying to go there and get three points. We are all excited for the game."
Rooney believes United's strengths are in the flanks and the striker believes delivery from wide areas could be crucial to his side's success at the Etihad Stadium on Sunday afternoon.
"I think our strength is getting wingers on the pitch, getting the ball out wide, attacking and getting crosses into the box," he said. "That's obviously the way Manchester United have played for years, so I think that's one of our strengths.
"Of course, they have a strong central midfield, but they also leave gaps out wide, so I'm sure Sir Alex [Ferguson] and Roberto Mancini will be looking at different things and ways they can capitalize on each team's weakness."