The daily publication state that Galatasaray are drawing up a shortlist of candidates who could replace Burak Yilmaz if he leaves for West Ham.
Sabah go onto state that the Istanbul giants have set aside funds to launch a bid for Remy who could be open to a move away from Stamford Bridge.
Remy is currently third choice striker behind Diego Costa and Radamel Falcao.
However, the France international has stated that he is happy to stay at Chelsea despite being their third choice striker.
“There are many reasons I want to stay but we won two titles (Premier League and Capital One Cup) last season and I am sure we are going to win more next season.
Umut Bulut will be Galatasaray’s only remaining striker if Yilmaz joins West Ham.
Remy – who has three years remaining on this contact with the Blues – provided two assists and scored nine goals in 29 appearances in all competitions for Chelsea last season.