Fletcher has netted nine goals to date this season and was an academy player at Hibernian during McLeish's spell in charge of the Edinburgh club.
McLeish said: "We've always fancied Steven. Even before he left Hibs we thought about taking him at Birmingham. It was round about the time when James McFadden came (January 2008). There was a kind of feeling 'should we go for Fletch' and then Owen (Coyle) took him to Burnley."
He added: "Maybe later on you say 'I wish we'd have taken him' but at the time we only had one choice. It was in my first transfer window at Birmingham.
"It would have been great to get him and James. James was flying when he came in and Fletcher would probably have been good for us if we could have got him as well."
McLeish was quick to spot Fletcher's ability even as a youngster at Hibs and has been impressed with his current form.
He said: "When I left Hibs, there were a few good youngsters there and Steven was one of them.
"He had a good touch and you can always recognise a kid when he's got talent in terms of their touch.
"I think he's definitely blossomed but he's always been a player who has had good confidence in himself and is flying now at Wolves."