That is according to BBC Sport journalist Sami Mokbel, who claims that talks are ongoing over a fresh deal for the Welsh international who is garnering Premier League interest.
Newcastle, Manchester United, Aston Villa, and Everton are all understood to have made "discrete enquiries" over Williams' future heading into the summer.
Forest are determined to keep Williams on Trent Side, and a new deal should prevent other clubs from prising him away.
The 25-year-old is currently tied down until 2029, but increasing his salary and length of contract should inspire him to remain at the club.
Williams has been integral to a Forest side that confirmed their safety in the Premier League and were knocked out by Aston Villa in the Europa League finals.
Across 51 appearances this term, the versatile full-back has scored twice and added four assists, with the PSFA once labelling his rise as "exciting."