The 60-year-old has yet to secure his first win as Forest's manager, taking over from Nuno Espirito Santo in September.
Despite facing chants of 'you're getting sacked in the morning' from fans after a 3-2 Europa League loss to FC Midtjylland, the club is reportedly standing behind Postecoglou.
Owner Evangelos Marinakis is reportedly using the international break to evaluate the situation, with a match against Chelsea scheduled for the next fixture.