A January move appears to be unlikely, but the giants will go head-to-head over the summer in a bid to lure the centre-back away from the Liberty Stadium.
Liverpool boss Brendan Roidgers is keen to reunite with Williams, having managed him during his spell as Swansea chief.
Despite taking Joe Allen from the club last summer, he has a transfer embargo blocking him from raiding his former team.
However, this expires at the end of the season, and the Northern Irishman is set to make a move as he looks to strengthen his defensive options.
But, he will face competition from Arsenal, with Arsene Wenger rumoured to see the Swansea skipper as the perfect man to add some stability to his back-line.
The Frenchman has been impressed with Williams’ robust style and sound technical abilities, and is willing to splash the cash to bring him to the Emirates Stadium.
Williams signed a new contract in October, but the Swans are preparing to receive a number of bids at the end of the current campaign.