The 30-year-old is in discussions with the Turkish Super Lig side after being deemed surplus to requirements by City manager Pep Guardiola.
The Brazilian made only five starts in the Premier League last season and was left out of the squad for the pre-season tour of the United States.
Fernando suggested last month that City would be willing to accept an offer of between $A10.45 million and $A11.9 million for his signature.
The midfielder moved to the Etihad Stadium for a fee in the region of £12m in June 2014 but has struggled to secure a regular spot in the starting line-up.
Galatasaray had been hoping to sign Marouane Fellaini from Manchester United but it is believed its interest has cooled after Jose Mourinho said he would not be sold.