The Galatasary boss handed Nastasic his chance in Premier League football last season, and the youngster impressed during his first campaign.
At 19, he was considered one of the most promising defenders in European football, however his form has dipped under Manuel Pellegrini this time around.
Now 20, Nastasic is no longer a first team regular at City, and Mancini is keen to try and lure him to Turkey.
The former City boss remains a big admirer of Nastasic, and with City expected to spend big money on a new centre back in the summer, Mancini remains confident of landing his man.
Nastasic is under contract at the Etihad until 2017, so the club would likely demand a hefty transfer fee.
Galatasary have money to spend however, with the club launching an ambitious recruitment drive with Mancini at the helm.
The Italian may however face a fight for his signature from former Liverpool boss Rafael Benitez, who is also reportedly keen on signing the young defender.