The Irishman has been out for a month with a hamstring injury but is now back in training and setting his sights on a return.
However, McLeish has been impressed by stand-in Brad Guzan and insists there are "no guarantees" his regular number one will automatically come back in.
The Scot told AVTV: "Shay is not far away. He is champing on the door to be involved this weekend against Everton.
"Whether he's going to make it, we will have to wait and see. He has made great progress.
"He is training with the group and it's a case of how sharp he's feeling and how confident he's feeling before we make a decision about him coming back into the team.
"There are no guarantees of that, obviously, because of the way Brad has played. Brad has been fantastic."