Clough, who guided the Brewers to a 2-1 Championship win at QPR on Saturday, is expected to meet Forest next week.
"I will think about it for a few days," Clough, 50, told BBC Radio Derby.
"It would be naïve for me to suggest there is no interest in a club I have had such a long association with."
Forest sacked Philippe Montanier as manager on 14 January and have identified Clough, who played more than 300 games for Forest and scored 131 goals, as a possible replacement.
He is in his second spell as Brewers boss and, like his father and Forest legend Brian, has also managed Derby County.
Clough met with Brewers chairman Ben Robinson on Friday to discuss Forest's approach and said he now had a "very difficult" decision to make.
"Timing in football is never good," Clough added. "It stinks at times, it really does.
"Whatever happens happens, but I can't tell you any more because I don't know what will happen. It is pretty obvious the dilemma. I will go away and think about it for a few days."
Clough had said in a BBC Radio Derby interview on Wednesday that links to the managerial role at the City Ground were "logical".
He said: "It's very difficult when you spent 18 years - I'm just over 50 years old - so a third of my life involved with a certain club.
"I've spent 11 with this one as well, but of course it's an easy link and a logical one from lots of points of view."
Forest are 19th in the Championship, five points clear of the relegation places and two points ahead of Burton, who have moved up to 20th spot.
Burton Albion boss Nigel Clough says he is interested in discussing the vacant managerial role at Nottingham Forest after being granted permission to talk to his former club.