The Red Devils clinched a record 19th league title in May, moving one ahead of their bitter North-West rivals, who finished the season in sixth place.
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But Rooney, who scored 11 Premier League goals for Sir Alex Ferguson's side last term, says the Anfield side have performed well in the summer transfer window, and have a chance of being involved in the title race.
"The main ones again will be Chelsea, Arsenal, Liverpool and Manchester City," Rooney said in The Sun when asked who he felt would be rivaling his side as they push for a 20th league crown. "One will push us as we defend our title.
"Liverpool have made some good signings. Under Kenny Dalglish I'm sure they will be trying harder than ever and will think they have a chance of the title."
United will also be looking to go one better than last season and add to their three European Cup titles in 2012.
The Red Devils were outclassed by Barcelona in May's Wembley final, succumbing to a 3-1 defeat to the masterful Catalan outfit.
And, while Rooney acknowledges his team were beaten by the better side, he is positive ahead of the new season and hopeful United have it in them to improve enough to match the Spanish champions.
"They were much better than us and deserved the win. But it's a long time ago now and we're looking forward to the new season.
"It was still a great achievement by us to get to the final but it's always disappointing when you lose. I hope we can improve."
