McLeish believes Savage will be doubly determined to do well against Blues if he is wound up by the taunts of their 5,500 travelling fans.
But he also knows Savage is capable of winding up the opposition and wants his players to keep their discipline as they strive to reach the quarter-finals.
McLeish said: "I like Robbie. I think he brings a little colour to the game. He has had a good career, he is a good player, a guy who rallies his team.
"Robbie has been playing well for Derby and he and Nigel Clough seem to have a great relationship. He is a great example for any young kid trying to make a career for himself in football, the desire to be something, when you see the fruits of what Robbie has done over the last few years.
"I was never a gifted player but my determination, will and drive allied to working with some very good people helped me and I am sure Savage will compliment his mentors, people he has worked with.
"He annoys the life out of the opposition and he can instigate a fight in an empty barn. He is good at that. Our players have got to have the maturity not to be taking the bait at all if Robbie is up to his mind games.
"We've got bigger fish to fry than having a spat with Robbie and getting involved in that. That will be taking our eye off the ball and not being professional.
"Robbie will use his mind games and experience and quite rightly. I would do so as well."
McLeish believes taunts from the Birmingham fans will only fire Savage up further.
He said: "I think he thrives on that. That is the sort of thing that motivates him. It would be better if the Blues fans never shouted his name at all and gave him a silent reception. Robbie would probably be surprised by that and not play as well."