Blues boss Alex McLeish has been tracking Traore for several weeks in the hope that Wenger would allow him to move to St Andrew's.
But Wenger will not decide whether or not to allow Traore to leave until the end of the August transfer window.
McLeish will now pursue other options although he may renew his interest in Traore at the end of the month if he is available.
McLeish said: "I've had a response from Arsene and it is not
positive because he is going to keep Traore in the meantime and won't make a decision on him until the end of the transfer window.
"I have to put the feelers out now and try and bring a left-back in because I have been playing right-footed people there, like Stuart Parnaby and Jared Wilson, which is not fair.
"Will I go back in for Traore? I'm not saying I won't go back to him. It is possible but depends what happens between now and the end of August."
McLeish is still interested in Spanish midfielder Michel although he insists no talks have taken place regarding a deal for the Sporting Dijon midfielder.
McLeish will have an opportunity to watch the player first-hand on Saturday when Sporting face Birmingham in a friendly at St Andrew's.
McLeish said: "I've watched the guy. I don't think that's any secret. But there is nothing cast in stone with anybody yet.
"It's not cut and dried that the board will give me money for that deal but we do need an injection of players in certain positions."