The Morocco international moved from the French side to the Emirates Stadium on a free transfer in 2010 but has struggled to adapt to life in the Premier League.
The summer arrival of Olivier Giroud and the form of Gervinho also means the 28-year-old is out of the first-team picture.
His old side are now ready to offer him an escape route out of north London, with the Gunners reportedly ready to cut their losses and get the striker of the wage bill.
Bordeaux's president Jean-Louis Triaud confirmed that they are considering preparing a bid to bring Chamakh back to the Stade Chaban Delmas.
"Chamakh could return. There is a serious chance," Triaud said.
"It is feasible for us and him but the choice is down to Arsenal. If he's not happy then we are in a position to talk about it."