Robinho believes Manchester City can emulate neighbours United as the teams prepare to meet at Eastlands on Sunday.
The Brazilian also claims Chelsea messed up a potential switch from Real Madrid which instead saw him make a shock move to the north-west for a British record £32million at the end of the summer transfer window.
The 24-year-old has already made an impact at City, scoring eight league goals including an audacious chip against Arsenal last week.
Now Robinho believes the team can become as big as the Red Devils following their takeover by the Abu Dhabi United Group, which has seen the likes of Kaka show interest.
He said: "In football, nothing is impossible. Manchester City might be classed as a small club but in two or three years' time, who knows?
"Three or four years ago Chelsea were considered a small club, but now they are a big club. Anything can happen. The project here is very ambitious and Manchester City will grow very quickly over the next few years.''
The forward pledged his future to the club, saying: "The only thing in my mind is to stay here for many years. Next year we will try our best to reach the Champions League.''
Robinho had been expected to move to Stamford Bridge but he claims they undermined the move by putting a picture of a shirt bearing his name on their website before the deal was finalised.
"It was Chelsea's own fault,'' he continued. "Everything would probably have been okay but Chelsea put that picture of me on their website and Madrid were upset about that.
"They didn't want to sell to Chelsea because they are in the Champions League and with me they would have been even stronger.''
Robinho claims he was badly treated by Real after reports he would be a makeweight in the deal to take Cristiano Ronaldo to the Bernabeu with the Brazilian going in the opposite direction.
"Things didn't end well in Madrid because the directors didn't behave properly,'' he added.
"I know what I'm worth and I don't feel I should be talked about as currency for someone else. Once a player finds out that he is seen as the bait in a part-exchange, how else can they feel? It's not the way to treat people.''