The 22-year-old has been on loan at Birmingham from Manchester City this season.
McLeish said: “We hope at some stage that City can give us a bit of goodwill.
“It would have to a loan deal because City have said under no circumstances will they sell Joe.
“City won’t be happy about me talking publicly about this but Joe has been tremendous.
“We want to keep him, we’d like to see him stay for another season. He wants to stay.
“City are his club, in terms of the ownership of the contract, and we respect that.
“They have a top class keeper in Shay Given and, unless someone comes in with a ridiculous offer for Given, you can see him staying at the helm with City for the next two or three years.”