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.
The on-loan Barcelona player left the ground on crutches and his chances of being ready to face the Gunners appeared to be slim.
But a scan on Monday revealed no ligament damage and now Hleb will await the results of a meeting with a surgeon in London on Tuesday before a final decision is made.
McLeish said: "It is not a ligament problem. Alexander had a scan yesterday and it is just severe bruising. He is seeing the surgeon in London today 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 tomorrow lunchtime.''
McLeish said: "Cameron has not trained yet this week but I believe he will be okay for the final and it is the same with Martin.''
The former Scotland 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.''