Williams, who scored 17 goals this season, has expressed his desire to move on while midfielder Dominic Blizzard failed to contact manager Gary Johnson before the offer he was made expired.
Middlesbrough loan duo Jonathan Franks and Jonathan Grounds have declined permanent deals despite being told they have no future at their parent club.
Meanwhile, Johnson has revealed captain Paul Huntington is still deliberating whether to commit his future to the League One club.
"Paul Huntington has been given more time to consider his offer due to a bereavement in the family and I am hoping to hear from him shortly," Johnson confirmed via the club's official website.
