Roberto Martinez will look after both the old and younger members of his Everton squad with new contracts in January.
Leeds chief Brian McDermott admitted earlier this week he tried to land a mystery winger on deadline day, only to see his price-tag end his interest in the player.
Clark has now confirmed he spoke to McDermott about Burke and he insists the Scotland international is happy to stay at St Andrew's, despite the interest from Leeds.
"I had a conversation with Brian on Sunday. He basically asked about Chris," said Clark.
"They (Leeds) said they were willing to do that deal, but thankfully Brian didn't come back and pursue it.
"Chris is 100 per cent happy and he's enjoying it here. He's never indicated to me that he has ever wanted to leave."