Ferguson, one of eight new faces at St Andrew's this summer after a £1.2million move from Ibrox, is preparing for a second crack at the English top flight.
The 31-year-old, despite a strong reputation north of the border, struggled to make an impact during an injury-affected 16-month spell at Blackburn that ended in 2005.
He re-established himself in Scotland again after that but controversy last season has brought him back to England.
Ferguson was told he would never be picked for Scotland again after indulging in a lengthy drinking session and then directing V-signs at cameras earlier this year. He was also disciplined by Rangers over the matter.
Ferguson this week criticised the Scottish Football Association over their handling of the affair but McLeish now wants him to concentrate on Birmingham.
"He has said his piece, I think he wanted to get some things off his chest," said McLeish, Rangers manager from 2001 to 2006.
"He feels he has been made a scapegoat.
"But Barry has got to look forward to his English career now, he has unfinished business.
"The jury might still be out in terms of his last stint in the Premier League, but the reports I got when I took him back to Rangers were that he was playing out of his skin.
"In that period after he bust his kneecap he came back to play a very important role for Blackburn."
Promoted Birmingham begin their campaign with a daunting trip to champions Manchester United tomorrow.
Their task is made all the more difficult by an injury crisis which has robbed them of defenders Liam Ridgewell, Martin Taylor, Scott Dann, Giovanny Espinoza and David Murphy.
Blues also have a number of other players missing but McLeish is not writing off the prospect of a shock win.
He said: "If you pass the ball and keep the ball, you can definitely get up the field.
"In terms of the squad I am still looking to enhance it but I know these fellas will give everything they have got.
"There is no reason why every player should be going there feeling nothing but belief in themselves and dreaming they can cause an upset against all odds."
McLeish will look for inspiration for the year ahead from Stoke's excellent survival campaign last term.
"We are looking to do a Stoke, to stay in the Premier League," he said.
"That is everybody's challenge and everybody's aim. I don't think we will look further than that."