The 19-year-old is yet to make his senior debut for the Blues, but has been propelled into the public eye this summer after claiming a place in England’s Euro 2012 squad before being selected by Stuart Pearce to represent Team GB at the Olympic Games.
Southampton have reportedly had an approach rejected by Birmingham, with Tottenham also thought to be contemplating a bid, prompting Clark to reaffirm his desire to keep the highly-rated youngster at the club.
"If other clubs want my players, I'm cool because it means they're good,” Clark told reporters.
“But it will take a crazy transfer fee for Jack to leave this club."
Birmingham start their Championship campaign at home to newly-promoted Charlton Athletic on August 18.