Ergun also stated that the club are considering signing the Togo international during the January transfer window.
“He’s been offered to us and we’re thinking about it,” Ergun was quoted as saying by HaberTurk.
Adebayor is currently a free agent after being released by Tottenham but has yet to find a new club.
The Istanbul based side are in the market for a striker as Galatasaray currently lack depth in attack. Adebayor would be able to play Champions League football should he join the Istanbul giants.
The Scorpions are doing well in the league but Galatasaray are likely to be the more attractive choice considering guaranteed European football and the likelihood of being involved in the title race this season.