Wales centre-back Williams, who is out of contract at the end of next season, has reportedly been the subject of a £4million bid from Sunderland.
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Swansea have been in talks with the 29-year-old over a new deal, but interest in Williams is thought to be high, with Napoli, Lyon, QPR and Arsenal all linked with a move for the former West Brom trainee.
And Williams' representative Jamie Moralee has suggested that Swansea may lose him for nothing if they do not agree an extension.
"Ash has only got one year left on his contract, so clubs will look at that," Moralee told BBC Wales Sport.
"If a new contract is not agreed or they don't accept one of the bids, Swansea could risk losing him for nothing.
"A bid has been made but nothing's been accepted or rejected yet - something has got to give.
"There are two or three clubs interested in Ash, and they must be confident in their ability to compete financially and be up there with Swansea in their offer for him.
"If Ash's contract does run down, it won't just be Sunderland interested. That will alert a lot of big clubs.
"Swansea hold the aces with Ash because they can keep him and give him a new contract, or they can sell him.
"Ash has to look for a contract that's right for him. He came to football relatively late and, as he's turning 30 this year, he needs a contract that can take him to 33 or 34.
"He has to look out for himself and his family - football is like any other business."