McLeish has been left frustrated by his recent attempts to bring more players to St Andrew's after seeing moves for Moussa Dembele and Charles N'Zogbia fail to materialise.
Striker Dembele opted to join Fulham instead of the Midlands outfit while Wigan forward N'Zogbia's wage demands reportedly brought an end to a potential £9million transfer for the Frenchman.
Ben Foster, Nikola Zigic and Matt Derbyshire have been the most notable arrivals at the club this summer and McLeish, who has been linked with Spartak Moscow captain Martin Jiranek, is confident that he will be able to add one more name to the Birmingham ranks by the time the transfer window shuts.
"We are trying our best to bring people in to improve the quality of the squad," McLeish told the club's website.
"The near misses I've had with Dembele, N'Zogbia and others, that's unfortunate when you see how good these players are but there are other ones out there and we'll try and add somebody before 6 o'clock on Tuesday."