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.
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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.