Williams flattered by Arsenal interest
Williams made 41 appearances as captain of Michael Laudrup's side last season as they finished ninth in the Premier League and lifted the League Cup.
His consistent performances have supposedly attracted attention from Arsene Wenger, but Williams claimed he is only concentrating on the new campaign at the Liberty Stadium.
"It means you're doing something right and people are talking about you at least," he told Sky Sports News. "I take it as a compliment.
"I don't really read the papers and that type of thing. You don't really know, as that's the future, and I can't really say. Different circumstances determine different things.
"I'm working hard trying to talk things through with the squad and the manager on the field, and trying to iron out a few things for the season.
"I don't know how you can go out there and not take it seriously. In terms of team selection, that's up to the gaffer, but if he's taking it seriously, then we all will.
"We'll just try and have a bit of fun and see where we can go with it. The league is our bread and butter, but any competition we're in we try and go as far as we can."