The 28-year-old has not played for Villa since rupturing ankle ligaments in February, but McLeish has hinted that the striker could be available.
"Can he make the Euros? Roy Hodgson would have a better idea. If there were six weeks of the season to go, he'd certainly be back within those six weeks," he told Sky Sports News.
"But whether he goes to the Euros would be Roy's decision. It seems at this moment that, with another two or three weeks' training, he could be fine and available, put it that way."
England boss Roy Hodgson will name his squad next Wednesday.