Madrid, who won a record-extending 14th European Cup in 2022 but lost to City in the semi-finals last season, open their Group C campaign at home to Union Berlin on Wednesday.
They will also face Serie A champions Napoli and Portuguese side Braga in the group stage.
"City are favourites because they have a squad that saw them win it last season and they haven't changed much. However in the Champions League, like always, there are surprises at the end," Ancelotti told reporters ahead of facing Union at the Bernabeu.
"Real Madrid are a team that are going to fight until the end. We never think of ourselves as favourites, just as I think City don't. They won it last year, they can win the Champions League."
Real may be taking on Champions League debutants Union, but Ancelotti stressed they would not take the Germans lightly.
"They're a new team in the Champions League but the fact they're here means they've done very well. They're well organised defensively, they're solid and they play with intensity...," he said.
"The Champions League is a special competition for us. We're going to treat tomorrow's game as something special. We want to get off to a good start in the group stage and we're playing at home."
The Italian added that Dani Carvajal (31) would be rested for Wednesday's game, but said the right back would likely be available for their LaLiga clash at Atletico Madrid on Sunday.
"Carvajal has a strain and we wanted to rest him to avoid problems," Ancelotti said. "He feels good and we don't think it's anything serious, so hopefully he'll be back soon.
"As things stand today, he has a chance of playing on Sunday. The player's general condition is pretty good. Lucas Vazquez (32) will play in place of Carvajal (against Union)."
