Postecoglou, 60, was sacked following Forest’s dismal 3-0 Premier League defeat to Chelsea on Saturday (October 18).
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The Australian had just eight games in charge at the City Ground, losing six and drawing two across all competitions before owner Evangelos Marinakis had seen enough.
According to The Athletic, Forest have already made contact with former Man City boss Mancini, 60, as an option to take over.
Mancini has been out of a job since leaving the Saudi Arabia national side las October, he also won City their first Premier League title.