McLeish has identified the left-back role as the one which is giving him most cause for concern with David Murphy and Franck Queudrue currently not fit.
Stuart Parnaby has switched from right-back to fill the position during the majority of pre-season.
McLeish said: "I don't want to upset Arsene Wenger by speaking (about Traore). I also see he has got a couple of injuries himself, like Gael Clichy, so I hope that's not ominous.
"We've got other targets but we want to bring in a bit of quality for the position.
"It's not a bottomless pit in terms of the money and we'd try to structure a deal on maybe a loan.
"I'm not talking necessarily about Traore, there's one or two options. It's better that I don't talk about other people's players at the moment.
"All that does is upset the Birmingham fans when we don't get them."
McLeish is also keen to bring in another midfielder, with Sporting Gijon's Michel understood to be on his radar.
The Spanish player is rated in the £3million bracket - the same as Aston Villa's Craig Gardner who has been another potential McLeish target this summer.