Robinson is a free agent and is therefore eligible to sign with the club under conditions of their transfer embargo.
The goalkeeper has been without a club since leaving Blackburn Rovers in the summer, and is claimed to already be on trial with the club, joining them for training.
Robinson made his name at Leeds United, coming through their academy system and playing in the Champions League, later joining Tottenham.
The potential deal emerges as Forest are preparing to play Leeds on December 27th, although there is no indication so far that a deal could be struck in time for him to play in the fixture.
Forest have been looking for back-up for Dorus de Vries since the summer, with a loan deal for Ben Hamer falling through in August. Forest are 15th in the Championship table at present, level on points with Robinson's most recent club Blackburn.
Robinson earned 41 caps for England in his younger days, and would likely be used solely as cover, but he would be an experienced back-up who is hopefully motivated to prolong his career for the love of the game.