McLeish, who played under Ferguson when he was in charge at Aberdeen, said: "City and United like to wind each other up and it has been quite entertaining to read the situation in the press.
"City had a dig at United with the Carlos Tevez poster and Sir Alex has responded. It is all part of this wonderful, crazy game of football."
McLeish is not sure City can usurp United's position as number one in Manchester.
"You had better ask Mark Hughes that but United have a pedigree of being champions and City are trying to get close to the feeling United have," he said.
"The proof of the pudding will be if City win something."
McLeish also feels there should be respect on both sides after recent incidents involving fans and players, two of them resulting in City duo Craig Bellamy and Emmanuel Adebayor hitting the headlines.
The former Scotland boss said: "The players can get dog's abuse and the minute a player reacts he is getting into trouble, not only with the footballing authorities but also the police.
"When I was at Rangers, before every game with Celtic we always got a letter reminding the players about their behaviour.
"There should be a bit of respect on both sides. The banter is all part of the game but, when it comes to filthy abuse it can become difficult for an individual.
"Some individuals have to show their emotions. Adebayor did it and apologised. Bellamy did it and he apologised. But they are big characters."
McLeish accepts the mentality of some people wanting big-spending City to fail is part and parcel of football.
He said: "I know what football is like. I've got a hard enough job myself without thinking about Manchester City.
"I know there is jealousy out there - not just for Manchester City but even for me. Some people want to see me fail. Some people are right behind me. It is just part and parcel of football.
"The little guy wants to see the big guy fail and Mark Hughes will be aware of that talk going on and will probably use it as a weapon for his advantage."
McLeish is working closely with City's new assistant chairman of football Sammy Yu in trying to bring new players to Birmingham in the January transfer window.
He said: "I have got to forge a close relationship with Sammy and so far that is working pretty well.
"We are looking at a lot of different players and now we have to produce a short list of people we definitely want to bring to the club.
"That is not something that will happen in a couple of days. But if it is a player that can enhance the team, we will try and get them to the club."
Birmingham left-back Gregory Vignal is back in contention to face City after overcoming a hamstring problem.
But he may have to be content with a place amongst the substitutes given the impressive form of Liam Ridgewell who has been converted from a central defender into the full-back role.
Winger Keith Fahey is again doubtful because of an ankle problem.