Birmingham owner Carson Yeung have previously promised McLeish plenty of money to spend, including “£20-40million” during the January transfer window.
McLeish said: “What we’ve already done is terrific. We are well down the pecking order in terms of facilities, money, infrastructure, and it is an incredible achievement already.
“Will there be more than £10million to spend this summer? It won’t be much more than that.
“We’ve got to be as prudent as ever and try and enhance the quality of the squad. We will try to get players (without spending too much) but you can’t keep pulling rabbits out of the hat.
“I heard Walter Smith talking about having a fantastic season at Rangers and then, because he’s done well on a limited budget, they think they can take a bit more away and he can do it again.
“I worked like that at Rangers as well and you can’t keep doing that. You can’t keep pulling rabbits out of the hat. There has to be investment and I am sure the board will back me.”
