McLeish's comments, made after the thumping defeat at ManchesterUnited, highlighted a growing rift between the Scottish manager and hisbosses after a frustrating January transfer window in which Birminghamhave missed out on targets Kenny Miller and Robbie Keane.
McLeish, who takes his side into a Carling Cup semi-final second leg against West Ham on Wednesday night trailing 2-1 from the first game, is working under strict financial restraints at St Andrew's and could see Stoke's interest in Jerome as the final straw.
He said last night: 'There hasn't been a bid for Jerome that I know of. Letting somebody go before we bring anyone in would be madness.
'Jerome is quick, he is strong, he has his positives. We have created chances this season but not been prolific in finishing them off.'
Instead, McLeish is eager to add a striker to a side who have scored just 21 goals in 22 games.
'We are still trying to bring in a face, particularly in the front area to bring a goal threat,' he said. 'You can only keep trying. God loves a trier and I will go right to the death to bring someone in to enhance the forward areas.
'People will ask after taking a drubbing today if it will affect our confidence. We were too apprehensive against United but we have a group of players capable of bouncing back.'
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