Roy Keane, Stuart Pearce, Alan Curbishley and Alan Pardew are other names in the frame.
Speaking to the Nottingham Evening Post, former Forest star Kenny Burns said: "Billy Davies did a superb job at Preston and then took Derby into the Premiership so his pedigree is good at this level.
"He will reward those with a good attitude who work hard and deliver what he wants.
"There would be no more Easy Street. And that is what it has been at the City Ground for far too long."