Like goalkeeper Joe Hart, who joined Torino on loan earlier, the former French international midfielder does not feature in new manager Pep Guardiola's plans.
Nasri, 29, joined City from Arsenal in 2011 and helped them win two Premier League titles.
Badly affected by injuries last season, he started only four league games, but came on during Sunday's 3-1 win over West Ham United for his 176th appearance.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Steve Tongue,; Editing by Neville Dalton)
