Cole's contract at Stamford Bridge is up at the end of the season and has reportedly attracted interest from Manchester United and old club West Ham United.
And Wenger admitted he is watching Cole's situation closely but added that strengthening the Gunners' midfield 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.
"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 [Alex] Song, [Abou] 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 [Cesc] 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."
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