The Mirror says McLeish has up to £40m to spend in the January transfer window from new owner Carson Yeung.
And he has turned his attentions to the Red Bull Salzburg hit-man after losing out on Milan Jovanovic.
Standard Liege striker Jovanovic is out of contract in the summer and Blues were hoping to tie up a deal for the Serbian international after he made it clear he is ready to quit Belgian football.
But Jovanovic has made it clear to Birmingham's negotiators that he is only prepared to move to a club in the Champions League.
McLeish will now try to lure Janko away from Salzburg and is considering a trip to watch the striker in Europa League action against Lazio tonight.