The Brazilian joined City from Real Madrid last summer for a British record transfer fee and he enjoyed an excellent start to his Premier League career.
Robinho has not scored since the start of the year but he is confident he will soon return to top form.
City are beginning to improve after a slow start to the season and Robinho feels he can realise his ambitions with the club.
"When I left Santos to (join) Real Madrid, all I thought about was becoming the best player in the world," he said.
"Today I am at Manchester City and I have the dream of fulfilling the dream of being the best player in the world."
Few Brazilians have set the Premier League alight but Robinho does not feel there is any reason why his countrymen should not succeed in England.
He said: "I hope to show the best football. Some players may be better or worse or different than me, but they didn't have luck here. Football means adapting.
"That doesn't mean that they don't have quality. Maybe one can end up in a country where they think football is easier and don't play well, or to a country which theoretically is said to be more difficult and show great football."
For more from Robinho, go to www.fobazo.com