Calderwood is also a target for Nottingham Forest and Hughton has confirmed Blues have been in contact with Hibs to express their interest in the Scotsman.
"It has been mentioned regarding Colin," Hughton told the Birmingham Mail. "We have had dialogue with the Hibs chairman and from that point we have done absolutely everything right.
"We are very conscious that he is their manager, very much so.
"Most people are very aware that I took Colin to Newcastle.
"He's somebody I know very well, he's a very good coach and of course I would like to bring him here. But I go back to saying that we are very, very conscious that he's the Hibs manager."