He has improved drastically having been with the Swans since their days in League One, and is central to the successful years Swansea are currently enjoying.
Williams has a number of years left in top-flight football, and retired footballer Robbie Savage has said that he would sign Williams if he were in charge of a top-six club.
Quoted on the BBC website, Savage said that the centre-half would not be with Swansea next season due to the interest in him.
However, these reports have not gone down well in Wales, with head coach Garry Monk rubbishing the claims that Williams could leave.
The defender is Monk’s first-choice captain and probably the first name on the teamsheet on matchdays, and he signed a new four-year deal with the club last summer.
Williams is an important figure in the dressing room, and represents something of an icon for the Swans, having been with the club since their days in the Football League.
Speaking in his press conference prior to the Premier League fixture with Tottenham Hotspur,and as quoted by ITV, 35-year-old Monk said: “Ash is massive for us and I think he’s been linked every year near enough to moving away. It was important that he signed a new long-term contract for the club last summer.
“He’s very settled here and loves the club. He stands for a lot of what we are doing and how I want to go forward with the club and the team, so I don’t envisage that changing at all.
"We’re under no pressure to sell and we don’t need the money. We want to add quality to the squad and not take it away and luckily we’re in a good position to do that.”
Swansea are in the situation where they can dictate the transfer business that goes on around them, thanks to being a well run club who are in no financial difficulty.
In the unlikely event of relegation, Williams would probably leave, but, while Premier League status is guaranteed, the centre-back will never leave the Liberty Stadium.