The 54-year-old Dyche has been out of work since leaving Everton in January. He was linked with the vacant manager’s job at Rangers last week, but sources have told BBC Sport he is unlikely to be interested in that role.
Forest, however, are likely to be of greater interest to Dyche, who lives in relatively close proximity to Nottingham and was a youth player at the club at the start of his career.
Former City Ground favourites Ian Woan and Steve Stone have also been long-term members of Dyche’s coaching staff during his managerial spells at Burnley and Everton.
Forest will not be required to pay any compensation should they move for Dyche.
Having already sacked Nuno this season and with Postecoglou’s possible dismissal likely to have financial implications, that could be a factor in the club’s choice of any replacement.