McLeish has already brought in eight players this summer in preparation for the club's return to the Premier League.
The Scot admits he has already spent more than he intended, but he still hopes to bring in new faces before the transfer deadline at the end of the month.
McLeish's next target is Sporting Gijon midfielder Michel, who could cost the club around £3million.
"We have made some contact and there are talks going on," McLeish said. "But it depends on the finances.
"We have spent more than the designated budget agreed at the end of the season.
"I had to do that, the board have seen the difference between last time in the Premier League and now.
"I would still like to enhance the squad further, whether the board can see themselves fit to do that, it is their decision.
"He has a lovely touch on the ball and I believe he could be a good asset, but we will be guided by the board's decision."
Promoted Birmingham begin their Premier League campaign with a daunting trip to champions Manchester United on Sunday.
McLeish's preparations have been hampered by a number of injury problems, particularly in defence.
Liam Ridgewell, Martin Taylor, Scott Dann, Giovanny Espinoza and David Murphy are all unavailable along with a number of other players.
"It has been frustrating," McLeish said. "There is no doubt I would have liked these lads to go into training at full tilt.
"It's not ideal but you hope to have a squad that can cover that - although if you were to have a squad that could cover this centre-half situation you'd need about 30 players, which is not on."
The injury problems mean new signing Roger Johnson could be paired with Franck Queudrue in the centre of defence.
Former Liverpool and Rangers left-back Gregory Vignal is set to make his debut after signing this week. New boys Joe Hart and Barry Ferguson could also feature but Lee Bowyer is suspended.
Ecuador striker Christian Benitez may have to make his much-anticipated debut off the bench as he recovers from a shoulder injury.
McLeish said: "I just want to make sure these new signings don't go into games not 100% fit.
"I know the attitude of these boys is brilliant, they want to be in there, but I don't want them to come in and not have that sharpness when the fans judge them.
"I'd like them to come in when they feel 100%."
McLeish accepts the challenge facing his side this weekend is a difficult one but he believes they are capable of pulling off a shock result.
He said: "At the end of the day United are a formidable side and on paper they should win.
"But if the bus rolls up to Old Trafford and the players have an adrenaline rush, as I always did when I was a player, that is what you are looking for.
"To compete with Manchester United is going to be very difficult but that is the challenge facing every team that plays them this season.
"You've got to play them some time but at the beginning of the season everyone is full of enthusiasm.
"That enthusiasm could be dampened by the end of the game but there is no reason why every player should be going there feeling nothing but belief in themselves and dreaming they can cause an upset against all odds."