The Blues manager is adamant he will not walk away from the club after persuading the likes of Serbian striker Nikola Zigic and former Manchester United goalkeeper Ben Foster to join his ranks.
McLeish has one year remaining on his current deal and, almost inevitably given Birmingham's top-flight showing last term, has been one of the names linked to replace Rafa Benitez at Liverpool.
But the Scot is relaxed about the contract situation, telling the Birmingham Mail: "These things take time but, if we can get it done in the next few weeks, it would obviously give people peace of mind.
"One or two of the players have been asking me what's happening, but I'm bringing in people like Ben Foster, Nikola Zigic - and I wouldn't do that and then say 'adios' the next day."
Birmingham City vice-chairman Peter Pannu added: "I have touched base with Alex's representatives.
"We have had initial talks and we will talk again."
Regarding the Liverpool speculation, Pannu said: "I don't respond to idle gossip or rumour.
"If any club approached us for our manager, I would deal with it then - and no club has."