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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.