Hart showed he has the credentials to be an international in a battle of the keepers with Craig Gordon at Sunderland.
Hart looks likely to bag a place in Fabio Capello's final World Cup squad but the Brum boss is not sure about throwing him in to the side.
McLeish said: "I want to see him play but it would be difficult unless he gets a few friendlies under his belt.
"I know what the scrutiny is like at that level, if he made a mistake, he would get killed. He's not ready to be killed."