The Gunners are said to have turned their attention back to Williams as they attempt to end a frustrating summer transfer window on a positive note.
Bringing in a proven centre-half would help to ease the pressure on Arsene Wenger, with the Frenchman set to be without Thomas Vermaelen for the start of the new season.
Williams is refusing to read too much into reports suggesting an offer from the Emirates is imminent, but concedes he would welcome the opportunity to compete on a UEFA Champions League stage at some stage in his career.
The 28-year-old Wales international told the Daily Mirror: "It's very flattering but you take it with a pinch of salt because you see a lot written and you never know what to make of it.
"I just take it as a compliment. You must be doing something right, whether it's true or not."
On his European aspirations, Williams added: "All players with any ambition want to see how high they can get, whether that's with their team - which has been the case with me at Swansea - or whatever really.
"If I sat here and said I didn't want to play in the Champions League, that'd be a lie. But I'd never disrespect a team I play for and say, 'that's it, I'm desperate to leave', just after a story in the paper. I'd never do that or think that.
"As professionals, you want to see how far you can go in your career, and competing for titles is where everyone wants to be. However you get there is a different story."