United sit top of the table on 33 points, one ahead of defending champions City, with Chelsea and West Bromwich Albion a further six points further back after 14 games.
Despite the furore surrounding the sacking of Roberto Di Matteo and subsequent appointment of Rafael Benitez, Mancini said Chelsea could not be ruled out.
"It's difficult to say this because the season is long and I think in February when the Champions League [starts] everything can change," the Italian told reporters on Friday ahead of Saturday's home match with Everton.
"I think Chelsea could win. In this moment I think [it's a three-horse race] but it's difficult to say."
Mancini confirmed England midfielder James Milner will miss Saturday's match with a hamstring injury he picked up in the 2-0 midweek win over Wigan Athletic.
He is a doubt for the midweek Champions League match with Borussia Dortmund and derby with United next weekend.
However, Mancini was hopeful that Mario Balotelli would kick on from scoring his first Premier League goal of the season against Wigan.
"Now I hope that he will continue to score because we need that, we need his goals," he said.
