Williams has lost his first team place at Goodison Park in recent times, and performances from the centre back have hardly convinced Everton fans he deserves to retain it. The Welshman has never replicated the form he was able to show at Swansea since making the move to the Toffees.
According to BBC Sport, Williams is open to a loan move to the Potters in the search for more consistent game time. The move would make sense for the central defender, who will be looking to rebuild his reputation following some inconsistent seasons.
The move from Stoke is yet another that signals their desire to return to the top flight at the first time of asking. The acquisitions of Tom Ince and Benik Afobe were statements of intent from the Potters, who don't appear to be shying away from spending their parachute payments to get them back to the Premier League.
The club also had a bid for Aston Villa's James Chester rejected recently and their business this summer doesn't yet appear to be finished.
It's understood that the Williams loan may not be the only business done between the two clubs, however. Sky Sports News are reporting that Everton are in talks with the Potters over a potential deal for midfielder Badou N'Diaye.
The Senegalese midfielder only joined Stoke in January, but it appears he is not looking to play in the second tier, and Everton are looking to take advantage.
The move for Williams would suit both parties, with Stoke in desperate need of some shoring up defensively, and Williams looking to benefit from being part of a positive, winning side for the first time in recent years.