The 33-year-old’s contract with Galatasaray expires at the end of the month and the Istanbul Giants have not offered Zan an extension.
Zan was been frozen out of Galatasaray’s squad this season and did not make an appearance for the Lion’s.
Eskisehirspor are understood to be preparing a contract offer in the region of €1 million per season.
Zan joined Galatasaray on a free transfer from Besiktas back in 2009. The experienced centre-back won three super lig’s, two Turkish cups and two Turkish Super cups during his spell at Galatasaray.
Galatasaray ended the 2014-15 season with 77 points following their 1-1 draw with Rizespor in their final game of the season.
The Istanbul giants will qualify directly for the Champions League group stages next season.