President Jean-Louis Triaud has opened the door for a move, although he says there has been no contact yet.
He told Sud-Ouest: "For me, we can talk about a return when the player or his agent picks up the phone and calls me. For now, it does not happen."
Chamakh won a Ligue 1 title with Les Girondins in 2009 and scored 61 goals in 251 appearances during his eight-year stint at the club.
The 29-year-old joined Arsenal in 2010 and scored 11 goals in his debut season, but he has become a peripheral figure since.