United take on Madrid in a two-legged last 16 tie later this month and a win would see them advance to the quarter-finals.
Mancini is happy for United to be successful as it will mean more games for them, while City can concentrate on clawing back the Red Devils in the title race.
"[Beating Madrid] would be another two games for them. I will go there and support them with a red and white flag," Mancini told reporters.
"But playing Real is tough, they are one of the best in the world. Them and Barcelona."
The City boss also insisted that his side can still win the title, despite being 10 points behind United ahead of their match with Liverpool this afternoon.
He continued: "If we could do it like last year when we were eight points behind with six games to go, it's not impossible that we can recover with 14 games left.
"We could recover five or six points and still lose, but we'll do everything to win this championship."
City take on Liverpool at 4pm today.