It looks likely that the 28-year-old will leave the Madejski Stadium, with the Royals unable to compete with the wages offered by other clubs.
Williams has made 156 appearances for Reading since joining from Bundesliga side Hoffenheim in 2013. He played the full game in Reading's penalty shootout defeat to Huddersfield in the Championship play-off final back in May.
If Reading came out on top at Wembley then it is likely that Williams would have signed a new contract for Jaap Stam's side.
“People always say I’m leaving every transfer window. I’m not going to lie I have had offers (in the past) but I came here and signed a four year deal for a reason.
“It’s not just words, I know what I have at this club, I think the fans know what I give to the club."
Danny Williams is considering his options after becoming a free agent
Huddersfield would be able to provide Williams the opportunity to test himself in the Premier League and give them more options in midfield.
Williams is predominantly a defensive midfielder but is able to play in a more advanced role as well as the right side of midfield. The versatility offered by Williams should be pondered by Terriers boss David Wagner.
After playing for a number of years in Wagner's native Germany, Williams has the ability to fit into the philosophy set in place by the former Borrusia Dortmund II head coach.
The potential signing of Williams would not cost the club a transfer fee and can comfortably afford to meet his wage demands now that the club are in the Premier League.