Sir Alex Ferguson's side face Jose Mourinho's defending Liga champions in the last 16 of the Champions League, and a win would keep them on course for another historic treble - albeit with more games to overcome.
With Premier League champions City out of Europe and now focused on the FA Cup and hauling back the Red Devils, Mancini is hoping the extra pressure on United will allow his team to mount another comeback like last season.
"[Beating Real] would be another two games for them. I will go there and support them with a red-and-white flag," he told reporters.
"But playing Real is tough - they are one of the best in the world," he added. "Them and Barca. They have incredible players, fantastic history. It will be very hard for United to beat them because they are a really top club.”While City need to beat Liverpool with their game in hand over United on Sunday to go seven points behind Sir Alex Ferguson's men, Mancini recalls last year's title race as inspiration for this run-in, with the Citizens hauling back an eight-point deficit to win the league on goal difference with the last kick of the season.
"If we could do it last year when we were eight points behind with six games to go, it's not impossible that we can recover this with 14 games left.
"We could recover five or six points and still lose at the end but we'll do everything to win this championship. United have good experience but anything can happen right up until the last game.
"And we have a good memory of what happened last year. When you are seven points behind, it's difficult to recover but we're a good team and playing well. We've also started to work better with the defenders."Mancini feels City are lacking goals this season, a problem which may be exacerbated by the sale of Mario Balotelli to Milan in the January transfer window.
"I don't know why they are not scoring as many. We're also missing Mario's goals. Last season, he scored 13 in the league and this season, he only got one.
"It's clear that we're missing seven, eight, nine goals and if we had got these, we probably would have four or five points more.
"We are disappointed because we lost two points against QPR but there are some games when you can attack for 100 minutes and you don't score."