McLeish is set to make wholesale changes for Tuesday's home Carling Cup clash with MK Dons, with summer signings Nikola Zigic, Matt Derbyshire, Jean Beausejour and Martin Jiranek all set to start.
Keith Fahey, Michel and Alexander Hleb will also be included in the starting XI as McLeish rests several members of his current Premier League line-up.
McLeish said: "It would be great to go all the way in the cup. Everyone would love a good cup run although the priority for us is the Premier League.
"But, having said that, I've got a squad of players I believe could be playing in the team every week. I've not got a first XI plus 11 reserves. I've got a whole squad that can play in the Premier League.
"But the guys playing tomorrow have got to show what they can do and put pressure on the ones who started at the weekend."
McLeish added: "I will be making a few changes. Players need games. Hleb still needs some match practice, Beausejour needs some pitch time and we want to look at guys like Jiranek who are new to the Premier League.
"But there are a lot of quality players playing tomorrow who could be in the first team. They've got to say 'I'll show the manager I'm worthy of a first-team place.' Fahey will start as well, Michel will start.
"The gauntlet is being thrown down to these guys to show what they can do.
"We are looking for the character and mental toughness to come to the fore in this kind of situation."
Birmingham will find out how long James McFadden will be sidelined with his knee ligament injury after he undergoes surgery in the next 48 hours.
McLeish believes the Scotland international was in the best form of his Blues career before the setback happened in training on Friday.
He said: "It is a shame because I felt James was coming back to his best. He was looking really bright in training. His fitness regime has been fantastic. He is eating the right things.
"I think this season would have been a huge season for him. Last season was his first full season and would have strengthened him physically and psychologically as well.
"To lose him at this stage is shame for James but hard on us as well."