The club's Managing Director was reportedly offered a similar post with Capital Radio but Blues' Chairman Gold has said that Ms Brady will not be leaving St Andrew's.
"Karren is staying," Gold said in an interview with BRMB Radio presenter Tom Ross before the game against Norwich.
"You cut her arm and her blood bleeds blue," he added.
"No doubt, she would have been extemely flattered about being asked to work for capital radio. I think she considered it but she is staying"