It is an undisclosed offer but speculation suggests it is £1 million. Burnley have responded immediately by turning the offer down. Kilby said: "I had an initial chat with Jez Moxey last week when they first expressed an interest and we told them he was not for sale.
"Today, Wolves have made an official offer for the player which has been rejected immediately. Kyle is very much part of our plans for the future and I reiterate that he is not for sale."
Kyle recently signed a new contract with the Clarets until 2010. When Celtic's offer was rejected in January they didn't come back realising it was a waste of time. The response given to Wolves should have the same effect, having been told that Kyle is not available.