The striker has been linked to Marseille, Juventus and Rennes.
But Wenger said: "Marouane is not going anywhere; there is not a problem with Chamakh.
"He is fighting for the position with Robin van Persie who is in great form at the moment. He will get his chance, we have so many games."
Chamakh said: "I love this club and I will do all I can to be a success here with Arsenal, I am working hard to reach my level."