But the Blues boss has stressed no player has a divine right to be part of the team whatever their quality or reputation.
Hleb has struggled for full fitness since arriving in late August on loan from Barcelona.
He was restored to the side for Saturday's 1-1 draw against Fulham and gave one of his better performances before suffering a hamstring injury.
McLeish said: "I've repeatedly told him (Hleb) that he is not fit enough to start games. He was disappointed not to start against Chelsea.
"He thought it was a slight and was a bit embarrassed by that. A top player thinks he can just walk into the team - but it doesn't work like that."
Source: PA
Source: PA