The Morocco striker, out of contract at the end of the season, was heavily linked with a move to the Emirates Stadium throughout the summer.
Arsenal had a bid turned down for Chamakh and Wenger had previously hinted he could make another offer during the winter transfer window.
"No, we don't go anywhere," said the Gunners' boss. "We have plenty of strikers. Eduardo has made a recovery and Nicklas Bendtner has extended his contract; that means we have strikers."