The 28-year-old has yet to make an appearance in either the Premier League or the Champions League for the Gunners this season.
"After Robin van Persie left, I thought I'd play more," he told French radio station RMC. "The competition is always a little hard in a club like that. I expected it.
"It's [up] to me to prove myself. But, in two [to] three months if nothing changes, then I must make a decision.
"With the departure of Robin, I'd say that I had a playing card. And if my playing time doesn't change, I'm not fooled, I'll go away."
Chamakh added that he could rejoin his old club Bordeaux.
"Bordeaux? It could be a solution if I decide to go," he said. "But my priority is to stay in the Premier League."
Chamakh joined Arsenal from Bordeaux in 2010.