This comes after the team's previous manager, Ange Postecoglou, was dismissed after eight winless games.
Postecoglou took over from Nuno Espirito Santo, who left the club earlier in the season.
Dyche's potential appointment would bring two former Forest players, Ian Woan and Steve Stone, back to the club.
However, Dyche has ruled out taking on a short-term deal, instead insisting on a long-term arrangement that would allow him to establish himself and his methods.