Birmingham recruited McLeish following Steve Bruce's departure, while Hutton secured an £8million move from Rangers to Tottenham in January - and the pair face each other for the first time this weekend.
"I wasn't really surprised," said Hutton. "It was totally understandable. It's a massive job coming here so it was a great opportunity for him, like myself, to be down here.
"Hopefully I can do really well and, hopefully, so can he."