The Serbian defender, who joined Roberto Mancini's side from Fiorentina on deadline day, has attracted comparisons to the Manchester United stopper early in his fledgling career.
|MANCHESTER CITY LATEST
|8/1||Manchester City are 8/1 with William Hill to win the Premier League and the League Cup
Nastasic told City's official website: "We didn't talk because I am aware of the rivalry between Manchester City and Manchester United.
"Of course we can have a chat off the pitch but we never talked about matters on the field."
Nastasic, who has already earned two caps for the Serbian national team, also revealed that international and now club-mate Aleksandar Kolarov helped convince him to join City.
He added: "When I heard about the possibility of my transfer to Manchester City, we did talk. He told me a little bit about his experiences.
"But there is still time. We are playing together for the national team so we will talk some more."