Whites boss Brian McDermott has previously stated that he attempted to sign an unnamed player during the transfer window.
Clark has confirmed that Burke was the player McDermott attempted to take to Elland Road.
"I had a conversation with Brian on Sunday. He basically asked about Chris," Clubcall.com quotes Clark as saying.
"They [Leeds] said they were willing to do that deal, but thankfully Brian didn't come back and pursue it.
"Chris is 100% happy and he's enjoying it here. He's never indicated to me that he has ever wanted to leave."
The 30-year-old winger moved to Birmingham from Cardiff City in 2011.