Forest owner Evangelos Marinakis sacked Nuno just three matches into the campaign and replaced him with Postecoglou.
The Australian failed to win a game and his dismissal – 39 days after his appointment on 9 September – meant his stint at Forest is the shortest permanent managerial reign in Premier League history.
Dyche was on the books of Forest as a youth team player in the late 1980s while Brian Clough was manager, but never made a first-team appearance.
He has not had a managerial job since being sacked by Everton in January after just under two years in charge of the Toffees.
Dyche won 21, lost 31 and drew 23 of his 75 Premier League matches as Everton boss, guiding the club to 17th and 15th-place finishes.
Prior to that Dyche spent nearly a decade as Burnley manager between October 2012 and April 2022, twice winning promotion to the top flight and helping the Clarets qualify for Europe for the first time since 1967.
He also had a stint in charge of Watford for the 2011–2012 season, only to lose his job following a change of ownership.
Kettering-born Dyche spent his entire playing career as a defender outside of the top flight, making more than 500 appearances for clubs including Chesterfield, Bristol City, Millwall, Watford and Northampton.