The 29-year-old was stretchered off with a knee problem during Saturday's FA Cup fifth-round victory over Sheffield Wednesday at St Andrew's but a scan revealed no ligament damage and now Hleb will await the results of a meeting with a surgeon in London before a final decision is made.
McLeish said: "It is not a ligament problem. Alexander had a scan Monday and it is just severe bruising."
He added: "He is seeing the surgeon in London and I haven't ruled him out for Sunday.
"Alex has great skill and massive experience and it is something I'd like to be able to call upon at some stage in the game if he is fit.
"We will probably know more by Wednesday lunchtime."
McLeish said: "Cameron (Jerome) has not trained yet this week but I believe he will be okay for the final and it is the same with Martin (Jiranek)."
The Blues boss is close to finalising his team to face the Gunners.
He said: "I'm pretty sure about the nucleus of the side and I know that some people will miss out but that is my job.
"I always pick my teams fairly without any influence from what players may say or what the media may say."
Source: PA
Source: PA