The Frenchman spent the last six months on loan at Bordeaux, and reports in the English media suggest the Ligue 1 club could try again to sign him.
However, reports in the Turkish media suggest Debuchy could be close to moving to Turkey.
According to Turkish journalist Gökmen Özdemir, who also works for Lig TV, Arsenal have accepted Galatasaray’s offer for Debuchy.
It’s not clearly mentioned if it’s a loan offer or permanent move, and that remains to be seen.
Özdemir says Galatasaray haven’t agreed personal terms with Debuchy yet, and that the player and his family are expected to make a final decision soon.
The 31-year-old has another three years left on his contract at Arsenal, and has managed only 12 league appearances in the last two years.