Press Association Sport understands thee Black Cats have made Swansea an offer in the region of £4million for the 29-year-old, who is yet to agree a new deal at the Liberty Stadium, prompting a flurry of interest.
Williams has a year left on his current contract, but could leave the Swans for free next summer if he does not agree an extension.
Poyet and sporting director Lee Congerton are currently in the process of reshaping the squad at the Stadium of Light with West Brom defender Billy Jones and Wigan midfielder Jordi Gomez already on board following the departures of Phil Bardsley and Craig Gardner.
In addition, Sebastian Larsson has agreed a new three-year contract, although fellow midfielder Jack Colback's future remains uncertain with derby rivals Newcastle among his suitors.
- Sports & Recreation
- Lee Congerton