Clarets manager Steve Cotterill has revealed that his club had rejected Fulham's offer for the 20-year-old Northern Ireland international striker.
"I had a conversation last week to say that the offer Fulham had made for Kyle wasn't acceptable, but it was made and it's still not acceptable," Cotterill told his club's official website.
"We don't want to sell Kyle come what may, but there would obviously come a time if it ever got to a certain figure that the club would have to look at it.
"Having said that we don't want to sell him, so we turned down Fulham's offer and are not anticipating another one."