The 47-year-old led Manchester City to their first top-flight crown since 1968 in May, pipping the Red Devils to the trophy on goal difference.
United have signed Shinji Kagawa and Nick Powell this summer but the Eastlands outfit are yet to strengthen their squad, leading Mancini to admit their derby rivals are in pole position to reclaim the title.
“United start as favourites this year,” said Mancini. “We are maybe in second, third or fourth position.”
The former Internazionale boss has grown increasingly frustrated at the lack of transfer activity at the Etihad Stadium this summer.
And Mancini appeared to blame City’s sporting director Brian Marwood for the failure to make any new signings.
“I don’t know what I should say in this situation because after three months, four months, I don’t know,” added Mancini.
“You have to speak to our sporting director, not me. I am not happy but I won’t say anything at the moment.”
Chelsea have been busy in the transfer window, signing Eden Hazard, Marko Marin and Oscar, while Arsenal have bolstered their ranks with Lukas Podolski, Olivier Giroud and Santi Cazorla.
And Mancini warned his City superiors that it would be foolish to be content with their title-winning squad, adding that City should not wait until late August to finalise potential deals.
“When you win something it is important to improve,” Mancini said. “But you should not buy new players 10 days from the end of the window. It should be two months.
“The championship finished on 13 May. You needed to buy players before now.
“Now it is difficult because there are some teams who can’t sell their players because they don’t have time to buy anyone else.
“The next 20 days is very difficult in the market.”
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