The young Scotsman's contract is due to run out in a years time and Forest boss Paul Hart may decide to cash-in on him now instead of losing him on a free transfer next summer.
Williams has attracted interest from a number of Premiership clubs and has expressed his desire to play for his boyhood team Glasgow Rangers one day.
Gazza is currently recovering from a shoulder injury and could well fetch between £3-5m should the Reds want to get rid of him.