Cole's contract at Chelsea expires at the end of the season and he has yet to reach an agreement regarding an extension with the Premier League leaders.
Chelsea's title rivals Manchester United have been mooted as admirers of the England international, while Tottenham Hotspur and former club West Ham United have been linked with a surprise swoop.
Reports have also claimed that Arsenal could make a bid for the schemer, but while Wenger acknowledges Cole's status as a free agent has some appeal, adding another creative element to his team is not a priority.
"Joe Cole is an interesting target, but do I have enough players in those positions? We shall see," said Wenger in the Daily Star Sunday.
The Arsenal manager has been happy with the performances of his midfielders this season and, with the likes of Alex Song, Abou Diaby and Denilson at his disposal, he no longer needs to worry about finding a replacement for Patrick Vieira.
He added: "First of all I must say that no matter how much money you spend to find a Patrick Vieira [it is hard to do]. Since I am in England, I hear 'this is the new Patrick Vieira' when a guy is tall and strong.
"But I believe strongly that our midfield are developing very well with Song, Diaby and Denilson because they are young, very young, but different to Patrick Vieira.
"I believe in them because if you compare them two years ago and this year they are tremendously improved and if they continue to play together, especially with Fabregas, they have a good understanding.
"I believe the midfield was not a problem this year because we created so many chances from midfield and we dominated nearly all the games in midfield. I don't think we had a big problem in there. I believe we had a problem of efficiency defensively."