Dyche, a 54-year-old former manager of Everton and Burnley, is currently in advanced talks with Forest. He has been out of work since leaving Everton in January, but the club has not ruled out other candidates yet.
Former Manchester City manager Roberto Mancini has also been approached by the club, according to previous reports.
Nottingham Forest is now considering Dyche as a potential replacement for Postecoglou. The club's search for a new manager continues, with several candidates in the running.