The North East outfit made an undisclosed bid for the 30-year-old last week – who has just one year left on his contract at the Liberty Stadium.
With Williams’ future seemingly uncertain, the defender’s agent Jamie Moralee insists that the Swans man wants to remain in South Wales but believes the club will have to offer their skipper a new deal.
"At the end of the day, we'll see what happens. A bid's come in from Sunderland, but I've got no control over who bids for my players and neither has the player," Moralee told the South Wales Evening Post.
"It's up to Swansea to make him an offer because he doesn't want to leave. Just because a club has put a bid in, that's not to say Ash wants to leave — that's far from the truth.
"There's been a lot of interest in Ash and that was always going to be the case, particularly as he only has one year left on his contract," he added.
"When players go into their last year it's dangerous. This is business, it's not personal. Hopefully we can get the situation put right for all parties."
Despite constant speculation linking Williams with a move away, Moralee believes his client will remain calm and evaluate his options carefully.
"Ash is fairly chilled about it as he has been for the last four or five transfer windows," Moralee said.
"Everything points to Ash wanting to stay. He's settled at Swansea, he's not far off 30 and not that far from a testimonial season.
"But he's got two kids and a third on the way.He has a family to support so the deal has to be right for Swansea and it has to be right for Ash. I'm sure a deal can be agreed.”