McLeish, who is happy to let his advisors thrash out the financial aspects of the deal, said: "We have started negotiations regarding a new contract. I have met Carson and (vice-chairman) Peter Pannu.
"They gave me some initial figures. I'll get my advisors now to meet with them and will let them thrash it out."
McLeish led the Blues to promotion last season and has helped to establish City in the top 10 of the Premier League this season.