Nasri has agreed personal terms with the Turkish club and the deal will be completed subject to international clearance being secured.
The former French international joined City from Arsenal in 2011 and helped them win two Premier League titles and two League Cups.
But he fell down the pecking order when Pep Guardiola became boss last summer and joined Sevilla on a season-long loan.
He played 30 times for the La Liga side but was forced to return to the Etihad at the end of last season.
Guardiola decided to take Nasri on the club's pre-season tour of America last month to put him in the shop window.
Nasri has been one of several stars Guardiola has been desperate to get rid of during the close season.
A club spokesman said: "Everybody at the club wishes Samir good luck in the next chapter of his career and would like to thank him for some fantastic memories."
