Williams has been a star of the Swansea side which has reached the final of the Capital One Cup.
The Daily Mail report that Brendan Rodgers is keen to bring his former player to Anfield, though Arsenal may prove an obstacle to those hopes.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?