The Serbia international is being tracked by Brum as he comes off contract in June.
McLeish told bcfc.com: "I've always admired Jovanovic but whether he's a player who can come here or not remains to be seen. I'm sure he's got many admirers but it's a shame that certain names get out into the ether because we try and keep as much private as possible.
"I feel uncomfortable talking about players. From the fans perspective if they see us linked with players like that it's brilliant, but I don't want to disappoint them because I could list another six big names that would excite them but if we don't get them you disappoint people.
"So I'd rather keep my business private and move forward."