The former England U21 coach made his name as a player at the City Ground, and managed the club for a short time in 1997.
Billy Davies was sacked on Monday after a run of eight games without a victory, and Neil Warnock says he turned down the chance to replace him following talks with the chairman Fawaz Al Hasawi.
Sky sources meanwhile say that Al Hasawi turned Warnock down because he wanted too much money, and was not the right man for Forest.
Gianfranco Zola is currently the favourite with Sky Bet for the job, ahead of second favourite Pearce, though the club is unlikely to make an appointment this week.
Warnock said the job might be right for Pearce, and the former England left-back admitted he would be interested provided there is no interference on football matters from the chairman or anybody else at the club.
"I have spent ten years training as a manager and that is what I am," Pearce told talkSPORT.
"There are some really good jobs out there at times that come up every now and again and Nottingham Forest outside the Premier League is an outstanding job for whatever manager wants it.
"I would have thought there are certain things a manager wouldn't accept. Things like picking of the team and players coming through the door who are signed by somebody else that you don't want.
"Those are probably the two golden rules for any managers. Some are different. Some accept that. It depends how desperate you are for a job. Some would accept that and some would want total control. It is varying degrees."