After losing his first-team spot at Manchester City to Shay Given last January, Hart has joined Birmingham on a year-long loan in an effort to gain greater experience.
A regular in Fabio Capello's squads until he was forced to play second fiddle at Eastlands, Hart earned a recall for last week's friendly in Holland once Ben Foster had pulled out with a minor knee problem.
Hart's hopes of retaining his place for next month's encounters with Slovenia and Croatia were given a significant boost on Sunday when McLeish selected the former Shrewsbury star ahead of Maik Taylor for Birmingham's narrow defeat at Manchester United.
"I know Joe's ambition is to go to the World Cup," he said. "What better incentive could he have?
"I have spoken to the English coaching staff. They like Joe, rate him highly and want him to do well.
"We know he is short of a bit of experience at first-team level but we are giving him that platform.
"Now it is up to Joe to keep the jersey."
Hart did well at Old Trafford on Sunday, making a string of saves to keep United at bay.
Even though he was beaten by Wayne Rooney, the 21-year-old should keep his place for Wednesday's encounter with Portsmouth.
However, with Taylor breathing down his neck, there is no chance of Hart becoming complacent.
"Maik was a little bit unlucky not to start because of his sterling performances last season," he said.
"Now it is up to Joe because I know there is a tremendous goalkeeper knocking at the door."