The Sun says the Arsenal flop, 28, continues to struggle in the Premier League after his free transfer from French football in 2010.
Now the Morocco striker is wanted back - either on loan or a permanent deal - but his £50,000-a-week Gunners wages ma prove a sticking point.
Bordeaux chairman Jean-Louis Triaud said: "There is a serious chance Chamakh could return.
"Money is the key question because salaries in the Premier League are enormous but it's also necessary for him to play.
"In December 2011 I sent a message to say the door was open for a return but he wanted to stay.
"Now the message is there again with the same objective."