Madrid have won eight games in row in all competitions, a run of form that has left them eight points clear as LaLiga leaders in Spain and top of Champions League group D ahead of their match with Inter Milan at the Bernabeu on Tuesday.
"I can't say if we're favourites or not, but I can say we can compete with all those teams," Ancelotti said in a news conference when asked about Liverpool, City and Bayern.
"With the quality and experience we have, we can compete. After that we'll have to wait and see.
"If you want to win this competition you have to face the best teams in the world whether it's in the last-16, in the quarterfinals... I think we can compete. I don't know if we'll win, but compete yes, for sure."
Madrid were outclassed by Chelsea in the Champions League semifinals last season under former coach Zinedine Zidane, having knocked out Liverpool in the previous round.
Ancelotti has won Europe's premier club competition three times already as a manager -- with AC Milan in 2003 and 2007 and with Madrid in his first stint in 2014 -- but said he's not thinking yet about lifting the trophy next May.
"So far I don't have that idea in my head," he said. "We're playing well, and tomorrow's game is one that we want to play: at the Bernabeu, against a strong team. Getting to the final is very difficult but it's the objective."
Speaking moments earlier, midfielder Casemiro had praised Ancelotti as "an icon" and said he was "surprised by how much he still wants to show he's the best coach in the world."
"Personally I don't have to prove anything to anyone," Ancelotti responded. "I have a young [coaching] staff with a lot of enthusiasm and desire to learn. We combine well, their enthusiasm with my experience."
Casemiro was asked about Madrid transfer target Kylian Mbappe -- saying he's been "in the top three in the world lately" -- and denied there would be issues fitting both left-sided wide forwards into the same team.
"Mbappe would be compatible with any player in the world," he said. "Mbappe and Vinicius, both are in incredible moments in their careers, I think they'd be compatible at any time. But he isn't our player."