Hart, on a season-long loan with the Blues from Manchester City, produced another exemplary display in Monday's 1-0 win at Stoke that extended the club's unbeaten Premier League run to 11 matches.
At a time when there is no stand-out candidate for the England number one slot, McLeish feels 22-year-old Hart is in with a shout of claiming the coveted position.
"His form has been brilliant, and let's face it, he is looking a big, powerful bloke between those sticks right now,'' remarked McLeish. "He has improved since he came to us. He probably had it there anyway, but we have probably brought out the potential.
"Joe has as good a chance as anybody else to certainly be in the England squad. I know that Fabio Capello and his staff like him, so he already has an edge, and his recent performances have certainly shown he can be a candidate.''
McLeish may yet launch a permanent swoop for Hart next month to avert fears of losing him in the summer.
Asked if he was concerned whether any fee might be too much come May, McLeish replied: "Possibly, but then maybe a bigger club might have their sights on him.
"We bring players in and try and improve them, and sometimes a situation like this arises. We've just got to keep going with Joe, and at the end of the season see what happens. He may feel he wants to come to Birmingham.''
That may yet force McLeish's hand, strengthened by transfer cash to be made available by new owner Carson Yeung, if the speculation is to be believed.
"We need to discuss that. We've not discussed it at board level,'' remarked McLeish at the suggestion he could pursue Hart next month.