The Wales international was linked with a £8m summer move to Arsenal this summer, as Arsene Wenger has reportedly lost faith in first-choice centre-back partnership Per Mertesacker and Thomas Vermaelen.
Williams has been excellent for Michael Laudrup's side this season, and led the Swans to the Capital One Cup trophy in February.
Laudrup recently signed a new one-year contract extension to stay at the Liberty Stadium, and Williams wants his teammates to follow suit by committing their futures to the club.
The 28-year-old is determined to build on the success achieved at Swansea so far, and revealed he's only concentrating on playing for the Welsh club, amid speculation linking him with an Arsenal switch.
"Can we keep the squad together?" said Williams. "Hopefully. We've got a good squad here, we get on really well, we enjoying playing.
"I cant speak for other people or for the future because it's football."
Arsenal's defensive problems have at least partly been attributed to the below-par performances of Vermaelen and Mertesacker. The two experienced internationals have come in for criticism this term, as the Gunners have fallen behind in the race for the top four.
They face Bayern Munich in the second-leg of the Champions League last-16 tie on Wednesday, hoping to overturn a 3-1 deficit.
Their defensive performance against the German giants was poor at the Emirates Stadium, and they'll need a much improved display if they want to stand any chance of progressing into the quarter-finals.
Williams has never played Champions League football, but the Gunners are thought to value his leadership skills, believing him capable of organising the Arsenal back-line.