Per the source, Bony is almost certain to leave the Etihad over the summer after being left out of the recent pre-season games and dropped from City’s Champions League play-off squad.
City boss Pep Guardiola is keen on trimming the squad after a busy summer signing several players and Bony is not expected to feature in his plans.
Bony did not feature against the Gunners in their recent pre-season friendly on Sunday despite being fit the play.
The Lions would be unable to match City’s asking price due to already facing a European competition ban for breaching FFP regulations.
Galatasaray are proposing that City loan Bony for a season to rediscover his form which could in turn increase the number of suitors willing to pay a higher fee for the Ivory Coast star.
Bony was one of the most highly sought after strikers in the Premier League at Swansea scoring 34 goals in 56 starts but he has managed to find the net just 10 times at City including only four league goals last season.
The 27-year-old striker does however, have another three-years remaining on his contract at City.