The former Forest defender, who came through the academy system under Brian Clough at the City Ground, has held several rounds of talks with Forest directors about taking charge.
Forest are seeking a third manager for the season after Saturday's dismissal of Ange Postecoglou. The Australian lasted eight winless games after succeeding Nuno Espirito Santo.
The Daily Express says Forest are now in talks with Dyche, who would bring former Forest stars Ian Woan and Steve Stone with him back to the club.
However, the former Everton manager has ruled out taking on a firefighter's post to the end of the season. Instead, he is insisting on a long-term deal, which would give him the chance to establish himself and his methods.
