The 28-year-old Wales international has attracted attention from a host of Premier League clubs, as he continues to impress in only his second season in England's top-flight.
Reds boss Brendan Rodgers knows Williams well from his time in charge in New South Wales, and reports suggest he could be planning to entice him to Anfield when the transfer window reopens in the New Year.
Liverpool boast a strong central defensive partnership already with Martin Skrtel and Daniel Agger, and have Sebastien Coates and club veteran Jamie Carragher in reserve.
But, Rodgers is believed to be keen to find a long-term replacement for Liverpool's record appearance-maker, as he enters the twilight of his career.
Williams tops the Premier League's defensive charts for blocks, interceptions and pass completion, so it's easy to see why he is a target for a number of sides, including Newcastle United.
With that in mind, Liverpool will face a fight to secure his signature, with Swansea boss Michael Laudrup equally eager to keep his captain at the Liberty Stadium.