Forest are looking for a new manager after Alex McLeish left the club by mutual agreement following just 40 days in charge at the City Ground.
A number of names have been linked with the position, but former Forest youth team player Dyche is thought to figure highly on the club's wanted list after impressing at Burnley and Watford.
Dyche caught the eye in his first league management role at Vicarage Road, leading the Hornets away from relegation trouble and to an 11th-place finish - their highest for four seasons before he was controversially dismissed to make way for Gianfranco Zola last summer after Watford were taken over by the Pozzo family.
The 41-year-old took over at Burnley at the end of October, replacing Eddie Howe at the helm, and he has made an instant impact at Turf Moor.
Dyche took over at Burnley with the side sat 14th in the Championship table, with 17 points from 13 matches, but since he has come in he has guided them to seventh spot, four points off the play-offs.
Dyche is regarded as one of the most innovative young managers in the country and Forest's owners see him as the ideal man to take the club forward.