The two clubs went head-to-head for most of last season and took the race right down to the final game of the season, with Sergio Aguero's 95th minute winning strike against QPR deciding the destination of the league crown.
However, ahead of the new term, the Italian boss believes Sir Alex Ferguson's side will be the team to look out for.
"I think United are the favourite team this year,” he told reporters. “We are maybe second, third or fourth.”
The Italian added: “I am confident with my players because we won the league and also because last year we beat a fantastic team like United.
|5/4||Manchester City are 5/4 to win the 2012-13 Premier League with bet365|
“But you do need to improve at every level. We are a young team and we need to get better, every month, every year."
With the season's traditional curtain-raiser against Chelsea in the Community Shield just days away, Mancini is nursing a few selection headaches ahead of the game, with the likes of Mario Balotelli and David Silva still requiring rest and Gareth Barry and Micah Richards consigned to the treatment table.
"Mario [Balotelli] and David [Silva] have had a busy summer, they need more time. They will probably be on the bench," he said.
"[Micah] Richards, I think will be out for just this game, he has a small ankle problem. Gareth [Barry], I don’t know. I hope that maybe three or four weeks, or one month, but I don’t know.”