Lamine Kone has rejected Sunderland's new contract offer.
Everton last week tabled a bid of £18million for the defender.
"We said we would wait until September 1, but we offered him a contract," said manager David Moyes.
"We gave that offer to him personally. His choice was still to go, to leave. He said, 'No' to the offer.
"We're disappointed, but he's still under contract for four years so it's not too big a deal to us. What he asked for was a new contract, and we offered him that.
"It's not a great scenario, but the player is ours. I've been in situations similar to this before. The players will go when we tell them to go – not when they want to go."