Forest sacked Postecoglou immediately after their 3-0 defeat to Chelsea on Saturday afternoon, as the former Tottenham boss failed to pick up a single win during his time at the club.
Reports suggest that Dyche has agreed verbally to take over as Forest's new manager, and now journalist Ben Jacobs has confirmed that he will only agree to take the job if he is offered a long term deal.
“Dyche made it clear in talks he would only take on the Forest role on a long-term contract. Forest view his style as a strong fit.
“Ian Woan and Steve Stone likely to form part of Dyche's backroom staff.”
Dyche was a youth-team player at Forest in the late-1980s, when Brian Clough was manager, and is said to live in Nottingham in what seems like the perfect fit for the English coach.
He has been out of a job since he departed from Everton in January this year, and could take control of Forest in time for their Europa League clash against FC Porto later this week.
Postecoglou was in charge for just 39 days after he replaced Nuno Espirito Santo in September in what is one of the worst appointments in Premier League history.