The former Arsenal star has been struggling with injuries since joining the Blues on loan from Barcelona in the summer.
Hleb sustained a knee problem during the 2-0 victory over Blackpool on Saturday, but will be ready for the clash with Villa.
McLeish told Sky Sports News: “He will be okay.
“He has not trained and we are finding that he is on the treatment table two or three times a week over the last three or four weeks since he joined us.
“That is a little bit frustrating because we are trying to get him to a level of fitness where he can get to his peak level and show what he really can do.
“He certainly showed glimpses of that last week in a very good game against Blackpool.”