The 19-year-old central defender, signed on deadline day from Fiorentina, has often been described as the "new Vidic" but he has not spoken to the Manchester United player.
Nastasic told City TV: "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."
One Serbian that Nastasic feels more comfortable speaking to is his national team and now City team-mate Aleksandar Kolarov.
Nastasic said: "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."
Source: team talk
Source: team talk