The 28-year-old defender is set to feature for the Swans in the Capital One Cup final at Wembley today, as he continues his sensational rise from the lower reaches of English football.
After an impressive first 18 months in the Premier League, Williams has established himself as a full international with Wales, and is now attracting admiring glances from some of the country's biggest clubs.
Red Devils boss Sir Alex Ferguson is keen to bring the centre-back to Old Trafford, where he could link up with close friend Rio Ferdinand.
Williams is under contract at the Liberty Stadium until 2015, having agreed a new £25,000-a-week contract with Michael Laudrup's side in October.
However, that is unlikely to stop Manchester United from pressing ahead with a move for the Swansea skipper, as question marks remain over the long-term future of Nemanja Vidic.
The Serbian stopper has suffered an injury-plagued couple of years at Carrington, and now Ferguson is looking for a potential replacement.
Although Williams would cost at least £10million, he is seen as a value-for-money acquisition, having proved he can cut it with the best in the Premier League.
Liverpool manager Brendan Rodgers is also a known admirer of Williams, having worked with him during his time in South Wales, and could rival Manchester United for the player's signature.