Postecoglou was sacked by Tottenham at the end of last season following a dismal Premier League season when they finished 17th.
However, the Australian led Spurs to a historic Europa League victory at the end of the season to end the club’s long-running trophy drought.
Forest currently sit 10th in the Premier League table after their opening three games of the season.
After 21 months in charge, Nuno’s last match in charge was a 3-0 defeat by West Ham before September’s international break.
The 51-year-old Portuguese coach took charge of Forest in December 2023 after the dismissal of Steve Cooper and helped preserve their top-flight status.
Last term he guided the club to seventh in the Premier League – their highest finish since 1994-95 – as they qualified for Europe for the first time in three decades.
BBC Sport understands Forest’s players have been caught by surprise by Nuno’s departure.
Many of them are on international duty and not due back for training until later this week.
But word spread, with some players hearing the news from other members of the squad.
It is thought Postecoglou will be appointed before Forest’s trip to Arsenal on Saturday.
He would become the eighth permanent manager since Evangelos Marinakis took over the club in May 2017.
