Clough is currently the bookies’ favourite to land the Forest job at the end of the season and the 50-year-old would reportedly be keen on a return to the City Ground.
Clough represented Forest as a player, and he would reportedly love the chance to work at the club again.
Forest owner Fawaz Al-Hasawi is in no hurry to appoint the former Derby County boss, but he could make a move at the end of the current campaign.
Clough is currently in charge at Burton Albion, and he looks on course to guide the Brewers to an unlikely promotion from League One.
Even the prospect of leading Burton in the Championship would apparently not be enough to convince Clough to stay at the Pirelli Stadium, though, if Forest did come calling.
The Nottingham Post also report that the Reds could land Clough without having to pay any compensation, due to a clause that he has in his contract at Burton.
Forest currently have Paul Williams in temporary charge, following the dismissal of Dougie Freedman earlier this month.