Forest are in the market for a right-back after giving up on their hopes of keeping Djed Spence at the City Ground next season.
The newly-promoted outfit have identified the Welshman as someone who could come in and fill the gap left by Spence in the team.
Nottingham Forest are serious about signing him and have put in a bid to test the water.
But it has been claimed that Liverpool rejected the opening offer from the newly-promoted side for Williams.
The opening bid was believed to be £11m and another £4m in add-ons, but it fell short of Liverpool’s valuation.
The Reds want more money and are holding out on a bigger figure when it comes to the guaranteed fee.
Steve Cooper is a fan of Williams and the defender wants to play for the Nottingham Forest manager.
However, Forest have work to do before they can agree on a deal with the Reds for the defender.