Everton had bid 10 million pounds ($13.32 million) for the 31-year-old central defender, according to British media.
Williams, who captained Wales during their run to the semi-finals of the European Championship, featured in 36 Premier league games for Swansea last season as the club finished 12th.
"We are not looking to sell him and therefore we have turned down the offer currently on the table," a Swansea spokesman told the BBC.
Williams is one of the most experienced central defenders in the English top flight having made more than 300 appearances for Swansea since joining from English lower division side Stockport County in 2008.
He played in all of his country's games and scored one goal at Euro 2016 in Wales' first appearance at a major international tournament since 1958.
Swansea begin the Premier League campaign with a trip to promoted Burnley on Aug. 13.
