The Blues manager is hoping the former Arsenal playmaker can make a telling contribution during the final six matches of the season - starting at Chelsea.
Hleb has ruled out a return to St Andrew's next season, claiming he is not suited to City's style of play.
But McLeish countered those comments by pointing to his side's Carling Cup final success over the Gunners.
When asked about Hleb's comments, McLeish said: "I'm not bothered what people are going to do at the end of the season.
"My focus is only on what is coming up, the next six games. That's my total focus. I can't be sidetracked by people talking about their future.
"The bigger picture is the Blues and that's my total focus.
"Alex is a terrific player. We haven't seen the best of him, but I'd like to think he has learned a bit about other aspects of the game while he has been in.
"If Alex can make a contribution in the next six games, we will take it. If he wants to go in the summer, we will shake his hand and wish him well."
Hleb believes he is more suited to the passing game of Arsenal and hankers for a return to his former employers.
But McLeish said: "The only other thing I'd say about Alex's comments is we have shown we can still beat a team like Arsenal in a major cup final when perhaps we are not the best footballing team in the world.
"Not many sides are like Arsenal and Barcelona but it shows a team with other qualities can do that (beat them).
"We can still pass the ball and we have done it well but we have adhered to some tactics that have served us well and we play to our strengths.
"We can play football. Look at guys like Barry Ferguson. They take care of the ball."
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