Dowie was dismissed by QPR earlier this season and is rumoured to have applied for the job which arose when Colin Calderwood was given the sack on Boxing Day after a 4-2 defeat by Doncaster Rovers.
Former Forest favourite Roy Keane who left Sunderland a few weeks ago would be the man many Forest supporters want, whilst Burton Albion boss Nigel Clough has also been linked with the job.
Simon Davey, Joe Royle and Billy Davies are also possible candidates.