Swansea boss Laudrup confident keeping Arsenal, Liverpool target Williams
He believes Williams will stay, particularly with the club having secured a spot in next season's UEFA Europa League.
"There is nothing to say," he told South Wales Evening Post.
"We know there will be rumours because the players have done well this season, but a lot of our players - including Ashley - have renewed their contracts this season and that is because they want to stay here I think.
"I am not saying that if a player signs a ten-year contract he will stay for ten years, but if you sign a new deal, I think you will stay for at least one more season.
"I understand the rumours with Ashley, but I think he wants to stay.
"Nothing has changed. I think they call it old wine in new bottles."