McLeish revealed Hleb has been able to train for less than 20% of the time available to him since his temporary move from the Nou Camp two months ago.
He has been affected by injury niggles but also a lack of pre-season action and looked a shadow of the player who was a key performer at Arsenal.
McLeish even left Hleb out of his starting line-up for the midweek 3-2 at Stoke and he remained on the substitutes' bench for the entire 90 minutes,
McLeish said: "Alex knows he is a big-time player and there are high expectation levels on him.
"He has got a reputation to preserve but he is not fully fit. He is not 100%. If Hleb was fully fit, we know he would be shrugging off the challenges on him.
"If we can get him top fit, we know that he will be a different player and a player who can make a difference. But I've got to do what is right for the team."
McLeish revealed: "Alexander has been here 70 days and only trained for about 13.
"We have to get that statistic higher to make sure he is at a level where he is going to make a difference for this football club. It just little niggles all over.
"The pre-season is crucial for players. If you don't get the right pre-season, the season can become a struggle for them.
"They can pick up niggles and Alex did not have much action pre-season at Barcelona.
"He said he did all the training but games-wise he didn't do much. He is about 12 games behind these guys here."
Birmingham started on a 15-game unbeaten run at this juncture last season and McLeish has challenged his players to start showing what they are capable of.
They were guilty of enforced errors during the setback at the Britannia Stadium.
But McLeish has stressed the need for there to be no panic over City's current plight as they lie 17th in the table after one win in the last seven games.
He said: "Time will tell if we can do that sort of thing again but we've proved we can do it.
"We've got different personnel this season but we have proved we can do it so why not?
"Everyone panics, the doom and gloom merchants appear and start to talk about the negative side of things.
"I know the way people spin things to try and put on a wee bit of pressure. But we are used to that.
"I've been in the game a long, long time and we just have to keep cool, keep calm.
"There is no reason why we can't go on a good run in the middle or end of the season. We have got the players."
McLeish has no fresh injury concerns ahead of Saturday's Premier League clash with Manchester City at Eastlands.
Colin Doyle is expected to again deputise as back-up keeper to Ben Foster while Maik Taylor recovers from a shoulder problem.
Full-back David Murphy could be in contention for a place amongst the substitutes after returning to training following a hamstring injury.