The Blues chief claims he is currently well-stocked in the centre-half department, with Roger Johnson and Scott Dann having shone for the Blues last season.
With that in mind, McLeish feels he would be better advised to strengthen in other areas.
France international Gallas is currently available as a free agent after parting company with Arsenal, but there is no chance he will be starting the 2010/11 campaign at St Andrews.
"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."
McLeish is still hoping to bring in at least two more players before the summer transfer window slams shut, but admits he may struggle to have them in place for next weekend's Premier League opener against Sunderland.
"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."