The Wales and Swans captain was reported to be close to agreeing a move to Goodison Park.
Williams, who turns 32 later this month, is under contract at the Liberty Stadium until 2018.
A club spokesman said: "We are not looking to sell him and therefore we have turned down the offer currently on the table."
Williams has played more than 300 games for the Swans since joining for £300,000 from Stockport in March 2008.
He has not played in any pre-season matches having been given an extended break after leading Wales to the semi-finals of Euro 2016.
There was reported Everton interest in Williams last summer when the Toffees' England international John Stones was being linked heavily with Chelsea and Manchester City.
With City still hopeful of signing the 22-year-old - valued at £50m by his club - Everton are seeking replacements in central defence.
Former Everton skipper Kevin Ratcliffe, who also captained Wales, says Swansea's stance could be more than just a bargaining position.
"It might be a determined decision to keep him because of the importance of the player," Ratcliffe told BBC Wales Sport.
"It's not just about the player being the player that he is but it's about his character and his leadership they're looking at and how do you replace that?
"I don't think they have and it will cost you a lot more than £10m."
Swansea City have rejected a £10m bid from Premier League rivals Everton for central defender Ashley Williams.