The Daily Mail are reporting that the Toffees will return with a £12million offer, after their initial £10million bid was rejected by the Swans.
Williams has been a star player for the club across three divisions, but is keen to have talks with Everton over a potential move. He has been the club’s permanent captain since 2013, and also skippered Wales during their stunning Euro 2016 campaign.
The 31-year-old played in 36 Premier League games last year, scoring twice, as Swansea saved a bad start to the season to finish comfortably clear of the relegation zone.
But new Everton boss Ronald Koeman is keen to bring him to Goodison Park, with doubt over John Stones’ future still ongoing.
After rejecting the £10million offer, all eyes are now on Swansea’s reaction, especially with their captain reportedly keen to discuss the move with the Toffees.