The daily sports newspaper states that the Istanbul Giants have established contact with the Senegal international with the view of signing him during the January transfer window.
AMK go onto state that Ba is willing to join Galatasaray if he is offered an equal contract to Wesley Sneijder.
Ba scored 29 goals in all competitions for the Turkish Super League outfit last season before joining Chinese giants Shenhua on a €14 million transfer over the summer.
The Mirror had linked West Brom and West Ham as being closely linked with the 30-year-old striker over the summer but he joined Chinese side Shenhua on a €14 million move instead.
Galatasaray currently find themselves in third place in the Turkish Super League with 29 points in 16 games.