The former Rangers boss is keen for his squad to remain focused on establishing themselves in the Premier League and does not want the inevitable transfer speculation to prove a distraction.
McLeish does not expect to blow Yeung's promised budget in the new year and believes the club's new board will have no problems if the cash remains in the bank.
"I won't be disappointed if I don't spend £40million or even £20million in January, and I wouldn't expect to," he told The Times.
"Despite making the claim that they are going to give us that to spend, I don't think they would be particularly unhappy with me if I spent less than that.
"They (the board) have got to get their results off the pitch. It's our job to get the boys winning football matches and that's hard enough."
McLeish knows that it will take time to redevelop his side and is aware that any big-money signings will have to prove their worth to the existing players.
He added: "It's a case of building brick by brick. Your squad will accept a big earner coming in if he's really making a difference."
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