Gallas is available on a free transfer after leaving Arsenal when his contract with the club expired earlier this summer.
The France international has been linked with a move to St Andrews, but McLeish insists he is not interested in the defender.
“No, definitely not,” McLeish told Sky Sports News.
“I have got two young centre-halves and it’s not the right move for me. I need to spend the club’s money on other positions that we really need to improve.”
But McLeish has admitted he would like to bring in at least two more players in the summer transfer window.
“We are hoping to do two or three before the deadline comes,” added the Scot.
“But if you are asking whether people will be in place before next Saturday, then maybe not, we might have to go with the group we have got.”
