The daily sports paper states that Galatasaray are yet to make a decision regarding the former Dortmund midfielders future at the club.
Galatasaray signed Grosskreutz from Dortmund last summer but were unable to register the 26-year-old after failing to send over the necessary paperwork to FIFA before the transfer deadline.
Grosskreutz will not be able to play for the Lions until next month when the transfer window opens.
The Red’s have reportedly agreed personal terms with Grosskreutz according to the Turkish newspaper Takvim.
Celtic have also joined the race for the World Cup winner according to the Scottsman.
Galatasaray travel to Izmir to take on Akhisar Belediyespor this weekend in the next round of Turkish Super Lig games.