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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.