The sports website claim that the Sweden international is close to agreeing terms with the Istanbul giants and is close to a move to the Turkish Super Lig.
Galatasaray have been on the hunt of a striker to ease the pressure on their top scorer Burak Yilmaz.
According to NTVspor Galatasaray are keen on the Sweden international due to his age. The Istanbul giants want to lower the average age of their squad this summer.
Everton, Watford and Norwich City are also understood to be interested in the 23-year-old.
Guidetti’s contract with City expired at the end of last month meaning he is be free to join Galatasaray on a free.
The Sweden international has 15 goals and 12 assists in 35 appearances in all competitions for Celtic this season.