The Northern Irishman coached the centre-back in his spell with the Swans, prior to taking the Anfield hot seat ahead of the current season.
After addressing the club’s attacking deficiencies with the additions of Philippe Coutinho and Daniel Sturridge in January, he has now set his sights on bolstering his defensive options.
Williams is reportedly Rodgers’ main target, and he is lining up a bid for the Welsh international’s signature at the end of the season.
With news that veteran Jamie Carragher is set to retire and speculation that Martin Skrtel could return to Zenit Saint Petersburg in a £12m deal, Liverpool’s rear-guard appears to be an area of uncertainty.
Rodgers is keen to bring in the man he worked with at Swansea and is confident that the 28-year-old will slot in seamlessly alongside Daniel Agger.
Michael Laudrup will be far from happy to lose his star defender, but the club may reluctantly accept Liverpool’s advances, as they did last summer with Joe Allen.
Rodgers is reportedly planning an overhaul of his squad at the end of the current campaign, with a number of first-team players believed to be surplus to requirements.