Davies, 47, led Forest to successive play-off campaigns while at the City Ground but had an uneasy relationship with the board and was sacked in June.
When asked if he would go back to work for a new regime, Davies told BBC Late Kick Off: "I'd be delighted to go back. I have great feelings for the club.
"I did want to get them to the Premier League. I'd love to finish that job."
Forest have scored just 22 goals in 27 Championship games this season
Forest, who have lost nine of their last 11 games, are third from bottom in the Championship and sit four points adrift of safety.
Manager Steve Cotterill took over from Steve McClaren in October but, despite an initial upturn in form, the Reds have been in woeful form of late and have scored just four-goals in their last 11 matches.
But Davies remains convinced they can turn things around: "I am sad to see what has happened," the former Preston and Derby boss added.
"But I wish them well and have no doubt they will get out of their troubles.
"The club deserve to be in the Premier League."

The English League One club are looking to replace Luke Williams who left the Wiltshire outfit last week after they were relegated.
Archibald has impressed The Robins owner/chairman Lee Power in guiding Thistle to a top six finish in the Premiership this season.
Partick Thistle say they have yet to receive an approach.
Archibald was approached by Shrewsbury in October but decided he had "unfinished business" with Thistle.
The 39-year-old is the longest-serving manager in Scotland's top flight and was in the four-man shortlist for the PFA Scotland manager of the year, won by Celtic's Brendan Rodgers.
Other names, who have been linked with the Swindon vacancy but appear to be out of the running, are the former Queens Park Rangers boss Jimmy Floyd Hasselabaink and Mansfield Town manager Stevie Evans.

Residents and an official said the victims were travelling in a pick-up truck that was targeted in the Hiran district of Hajja province.
They had been heading to a local market, according to the residents.
There was no immediate comment from the coalition, which is fighting the Houthi rebel movement in a bid to restore the internationally recognised government.
The coalition says it does not target civilians, but the UN says air strikes have caused the majority of the more than 4,125 civilian deaths recorded since the conflict in Yemen escalated in March 2015.
Wednesday's incident comes two days after a 48-hour cessation of hostilities ended.
Both sides accused each other of repeated violations of the truce, which brought a brief respite from air strikes for residents of the rebel-controlled capital, Sanaa.
Fighting continued in and around the south-western city of Taiz throughout the weekend, however, and on Tuesday clashes there reportedly left 11 people dead.
Military officials said pro-government forces had repelled an attack on Taiz's western outskirts by Houthis and allied security personnel loyal to former President Ali Abdullah Saleh.
The International Committee of the Red Cross expressed alarm on Tuesday at the situation in Taiz, where some 300,000 people have been under siege by rebel forces for more than a year.
"Sniper fire and indiscriminate shelling has trapped civilians. Dead bodies are in the streets and people are unable to attend to their most basic needs. The situation is desperate," said the ICRC's head of delegation in Yemen, Alexandre Faite.
Mr Faite added that the main hospitals in Taiz had reported receiving an average of 200 wounded in three days. Many patients were suffering from blast injuries and had to have limbs amputated.
Ex-Nottingham Forest boss Billy Davies says he has "unfinished business" at the club and would love to return.
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Partick Thistle manager Alan Archibald is on a shortlist of candidates for the Swindon Town vacancy.
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Twelve civilians are reported to have been killed in a Saudi-led coalition air strike in north-western Yemen.