Pearce turned the job down last week, citing personal reasons, but it is understood that the Sky Bet Championship club are now in talks over a longer contract offer.
Malky Mackay, Steve Clarke, Roberto Di Matteo, Neil Warnock and Gianfranco Zola have also been linked with Forest since Billy Davies' departure last week, but it appears Pearce is now owner and chairman Fawaz Al Hasawi's clear first choice.
Former England U21 manager Pearce, who spent 12 years with Forest as a player, told Sky Sports News on Friday: "I had a chat with the owner and I was very impressed with him.
"He came across really well with a real passion for the football club but I said to him I didn't want to take those negotiations any further on the grounds that I had one or two personal issues that I had to put in place first, so it went no further than that.
"But I must say I was very impressed with him. He came across really well and obviously I have got my fingers crossed that they get in the play-offs and have a good push for the Premier League this year.
"It was the right time not to pursue it, but it was nice to be talked about and obviously nice to have a chat with the owner of a club that is very close to my heart."
Pearce, 51, was also caretaker manager at the City Ground during the 1996-97 season before going on to manage Manchester City from 2005-07 following a spell as coach.
Al Hasawi told Sky Sports News on Thursday: "Stuart Pearce is one of the legends of Nottingham and he is welcome to come any time to the club.
"Maybe he is one of the list of names we wanted for this club and I don't know about him at the moment and his situation to be honest, that he might take the job or not.
"But he is most welcome at any time to come to this club because he is one of the legendary Nottingham Forest players."
Forest are currently seventh in the Sky Bet Championship, two points below sixth-placed Reading with seven games remaining.