A deal is understood to have been struck for £12million and the transfer could see Stefan Savic move in the opposite direction after failing to fulfill expectations at the Etihad Stadium.
Nastasic, a Serbia international team-mate of Manchester United captain Nemanja Vidic, has long been linked with City and they will now push for an agreement on personal terms and a medical before Friday’s deadline.
The 19-year-old only joined Fiorentina from Partizan Belgrade last summer but he has made 25 appearances for the Italian club as they finished 13th in the 2011/12 Serie A.
City boss Roberto Mancini will hope Nastasic will prove a suitable improvement on Savic, who has endured a difficult time since moving to England in July 2011.
A fee of £6m was paid to Partizan but the 21-year-old has made just five Premier League starts for England’s reigning champions.