"We'd still like to enhance it, the board are right behind me on that which is fantastic," McLeish told BBC WM.
"We've brought a couple of players in, we lost a few at the end of the season, I think we could be enhanced a bit and the board are pulling out the stops."
Over the summer Blues have seen Joe Hart return to Manchester City after a year's loan, while Lee Carsley, Christian Benitez, Gary McSheffrey, Franck Queudrue and Gregory Vignal have all moved on.
"There's no doubt we'll try right to the wire to bring in one or two more bits of quality," McLeish insisted.
"We have been talking for quite some while now with players and agents and clubs, and we'll keep on talking.
"The board are well aware of where I've identified players and we will try and do what we can to make Birmingham as potent a force as we were last season."
Blues open up their Premier League campaign at Sunderland on 14 August.