The Gunners were initially interested in the Chelsea discard when he was still contracted to the champions but then pulled the pin, handing the reins to Tottenham who seemed to be certainties to secure the 28-year old.
However, it is believed that Wenger has made moves to bring the ex-West Ham man to the Emirates although he did shy away from any transfer talk when quizzed on the situation.
"I like him (Joe Cole) as a player because when he played against us he always did a lot of damage," said Wenger.
"He can create impact through his creative play. He can dribble, he can pass, he can score goals."