McLeish is relaxed about the situation and still has 12 months remaining of his current deal.
But his advisors have now made contact with Blues vice-chairman Peter Pannu, who is conducting negotiations, and the former Rangers boss is optimistic the situation will be resolved sooner rather than later.
Former Blues manager Trevor Francis has already claimed McLeish would be "Birmingham's biggest signing" of the summer given his record during the past two seasons.
The 51-year-old steered City to promotion from the Championship 12 months ago and then a top-10 finish in the Premier League.
McLeish said: "What is the situation with my contract? Peter Pannu has been a little bit busy and my guys (advisors) were a little bit busy before.
"But they have made contact now and I'm hoping that something can get done fairly quickly.
"I don't envisage any hold ups. It doesn't matter, I am still contracted for another season anyway.
"Hopefully we will get things tied up."
McLeish laughed off Francis' comments and joked: "I meant to make a public announcement that Trevor is my new agent."
The ex-Scotland coach is stepping up his bid to bring a new striker to St Andrew's and has been linked with a move for Valencia's Nikola Zigic who could cost around £6million.
McLeish said: "We are making progress in the striking department. We are going to have to be patient.
"I can't divulge any names at this moment but we are making good progress on three or four names."
Birmingham have also been monitoring Wigan's Charles N'Zogbia and reported to have had an £8million bid rejected.
McLeish said: "I really don't want to speak about that (the N'Zogbia bid) publicly. The club would need to make those statements.
"I think it's better that we keep our business private until we have something to announce."