The 19-year-old Serbia international is expected to move to the Etihad Stadium after impressing in his debut season in Serie A, with manager Roberto Mancini said to be a long-term admirer of the former Partizan Belgrade player.
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City are believed to have offered around €11m (£9m) and Stefan Savic for Nastasic, although Fiorentina are hoping for another €6.3 (£5m) in add-ons.
A deal nonetheless appears to be imminent and sources expect it to be announced in the next 24 hours.
Mancini has been looking for more central defensive cover after Montenegro international Savic failed to adapt to the Premier League in his debut season.
Nastasic made 27 appearances for Fiorentina last season after arriving from Partizan and was spotted by City scouts watching Stevan Jovetic, as revealed by Goal.com last week.
But while the deal for the 22-year-old playmaker appears to have stalled, Nastasic should become only the second new signing for the Premier League champions after the arrival of Jack Rodwell earlier this month.
Savic could depart the club after arriving for €7.6m (£6m) last July and having made only 11 Premier League appearances for City.