McLeish started talks over a new deal before the end of last season after steering City to promotion and then establishing them in the top flight.
But it is only now the former Scotland boss appears ready to put pen to paper on a new deal.
McLeish, whose side entertain Liverpool on Sunday, said: "Talks have progressed and I'm just inches away from signing a new contract.
"The figures and everything are fine. We've just got to iron out the rough edges.
"We're pretty close and there are just a couple of technicalities - a release clause and that kind of thing - but it's not excessive from either camp and it's absolutely standard.
"Contracts are not something I like talking about in public, but it will be nice to get it resolved."
McLeish admits the talks appear to have taken longer than expected to be concluded.
He said: "I think it was just the timing of the announcement that we were going to have talks in the middle of a hectic season.
"We've kind of let things peter out until the end of the season and then we couldn't pin a date down because either my representatives were busy or (chairman) Peter Pannu's side was busy.
"That kind of wasted a lot of time, but, to be honest, we've only really sat down four or five times to talk about it."
McLeish has not ruled out recent signing Aleksandr Hleb for the game against the Reds despite him suffering a leg injury when on duty for Belarus against Romania in midweek.
And the City manager believes the former Arsenal player could have the same sort of influence as Christophe Dugarry, who spent a successful spell at St Andrew's under Steve Bruce.
McLeish said: "He has the capabilities of doing that. His team-mates will want to show him how good they are.
"I saw him play for Belarus against Scotland a couple of times. They actually beat us once at Hampden Park and, on that day, he was very influential.
"We needed new players. We needed them because, if we get injuries or suspensions, we would leave ourselves short."