"Chelsea came to me with a good offer and they are huge club. On top of that, they had a coach in Big Phil (Scolari), for whom I have the biggest respect," Robinho told the Daily Express newspaper.
"I'm sure that one day we can rival clubs like Chelsea. We are a very ambitious club and many people underestimate us.
"We may not be the biggest club yet, but let's not forget where Chelsea were a few years ago. We can do as well as they've been doing in recent years.
"Manchester City are aiming for big things and with the new wealthy owners anything is possible.
"We want to be up there and maybe win the Champions League one day. That's the ultimate aim."