There's talk Hart will start next week's friendly against Egypt.
McLeish admitted: "It would be good to see Joe getting a crack because he has been excellent for us. There is absolutely no hiding place if you play at international level.
"He's going to get scrutinised in every single part of his game. But I think he's got the temperament for it. The next four World Cups are there for him.
"This one might be a bit early for him and I suspect that Fabio Capello will lean towards the experienced guys. But Joe could certainly be on the plane."