The Blues, who today, smashed their record transfer fee to sign Ecuador striker Christian Benitez, have been trying to sign Cardiff's Roger Johnson and had bid £3.5m which has been rejected with The Bluebirds saying that he is not for sale.
It is understood that if Birmingham don't get Johnson then they will look elsewhere with Dann who Birmingham had watched on a couple of occasions being on their radar.
Dann is one of four players currently in discussions with the club about a contract extension.