Mauricio Pochettino has ruled Tottenham out of contention, but Wenger will not be doing likewise despite Saturday's 3-1 loss to Manchester United.
The Gunners, who last won the trophy in 2003-04 and have three more points than rivals Spurs, are 15 points behind leaders Manchester City after five defeats in their first 15 games.
"I am not Pochettino, I am Arsene Wenger," the Frenchman said. "I am here to fight as long as I can. As long as mathematically it's possible you have to fight. You cannot give any other message out."
Despite a title bid appearing unlikely for another year, Wenger welcomed the positive reaction of the Emirates Stadium crowd to Arsenal's performance in a breathless bout.
He added: "The crowd sees as well that the team produced what is expected from them.
"The crowd was outstanding. And the team was outstanding. But, we were not efficient. I cannot deny that. They have scored three, we have scored one."