Per the source, Gunners boss Arsene Wenger is under pressure to strengthen his attacking options this season after a disappointing campaign from Olivier Giroud.
The North London based outfit have yet to bring in a big name striker after being closely linked with Jamie Vardy and Lacazette.
City manager Pep Guardiola has no plans for Bony last season and was left out of recent pre-season games and dropped from the Citizens Champions League play-off squad.
Besiktas have an impressive record in turning around the fortunes of once highly rated experienced strikers.
Mario Gomez looked down and out at Fiorentina but a season at Besiktas saw him finish as top scorer, win the league and earn a place back in the Germany national team as first choice striker.
Arsenal are however, favourites to sign Bony before the window closes after the odds of a move to the North London were shortened to 6/4 with Betstars.
Bony has managed to find the net just 10 times at City including only four league goals last season buy he does have another three-years remaining on his current deal.