The 5-0 hammering at Manchester United has left Blues in the thick of a relegation fight, with added uncertainty over whether McLeish will be able to make further signings before the transfer window closes.
The Scot is certainly not keen on the idea of losing Jerome, even though the forward was only a substitute at Old Trafford.
"How can we let someone go when we have not even brought anyone in," said McLeish. "It would be madness.
"Jerome has these positives. He is quick and strong. We could do with getting someone else in who can compete for a place in the side alongside him as well as the other strikers.
"We have created chances this season but we have not been prolific in terms of finishing them off."