The Mirror reports that the Reds will make a mvoe for Williams if Daniel Agger joins Manchester City.
New Liverpool boss Brendan Rodgers have worked with Williams at Swansea for the past two seasons.
Liverpool are reportedly prepared to sell Agger for around £23million.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.