Forest manager Joe Kinnear told SkySports: "If we get between £4m and £8m for him, I could use that on new players."
Chelsea, Tottenham, Blackburn and Birmingham have also been linked with the left-sided midfielder but it will take a bid of over £5m to tempt Chairman Nigel Doughty who would also want a sell-on clause installed.
Reid scored Forest's opening goal in their 2-1 win against Bradford on Saturday to help the Reds to their first win in four months.