Gianfranco Zola, Roberto Di Matteo and Chris Hughton are among the leading candidates under consideration by owner Carson Yeung and acting chairman Peter Pannu after McLeish resigned on Sunday.
In the frame: Cotterill, Zola and Hughton are in line to replace McLeish
But reports that Birmingham have already asked permission to speak to Portsmouth boss Steve Cotterill are wide of the mark.
LATEST ODDS Hughton 5/2
Di Matteo 8/11
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Birmingham are eager to make an appointment as quickly as possible as they have to prepare for a Europa League campaign in addition to trying to gain promotion from the npower Championship.
Pannu said: 'I am discussing the situation with Carson and we hope to install the new man as soon as possible. There are at least six (candidates) on the radar.'
Former Newcastle boss Hughton is the number one choice of Birmingham fans in a poll conducted by the Birmingham Mail newspaper.
Moving house: McLeish resigned as Birmingham City manager on Sunday
But Di Matteo and Zola are also free agents after their previous spells as manager of West Brom and West Ham respectively.
Meanwhile, Birmingham are set to complete the signing of Morgaro Gomis from Dundee United on a free transfer despite McLeish's departure.
Pannu said: 'Gomis is still coming in to Birmingham.'
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