This comes after the Pitmen received a seven-day approach from Welsh Premier side Airbus UK Broughton for his services last week.
An energetic, creative midfielder with considerable experience at National League level, he joined the Pitmen following a successful trial in August 2015 after being released by Altrincham at the end of the 2014/15 season.
Williams has been an integral part of the Pitmen`s first-team squad this season, scoring four times and also putting in a number of man of the match performances.