Southampton will not accept offers for forward Jay Rodriguez or midfielder Morgan Schneiderlin this summer.
Everton forward Kevin Mirallas has hinted that he will sign a new contract at Goodison Park in the summer.
Williams, whose contract is set to expire at the end of next season, has been linked with a move away from the Liberty Stadium, with the likes of Arsenal, Napoli and QPR reportedly interested in the 29-year-old.
The Wales captain is thought to be on holiday in Sardinia following the end of the Premier League season, while his agent Jamie Moralee is at the World Cup in Brazil.
Williams, who has been linked with a move to Liverpool in the past, joined Swansea from Stockport in 2008 for a fee of £400,000.
Talks have been ongoing to renew Williams’ contract as Swansea hope their captain follows in the footsteps of goalkeeper Michel Vorm and striker Michu in signing a new deal with the club.