Birmingham made an enquiry about McGeady's availability earlier this month but were told the 23-year-old was not for sale.
"Aiden's a very important player for our club in what we're trying to build here," explained Mowbray.
Responding to reports of a possible fresh approach from Birmingham, he said "there's no interest whatsoever in listening to bids".
However, BBC Scotland has learned the Premier League side are preparing to increase their offer to sign the Republic of Ireland international.
Croatian striker Jelavic, who scored three times against the Celtic in this season's Europa League group stages, said he would prefer to stay in Austria until the end of the season.
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