Davies and his representatives were in negotiations with Forest chairman Fawaz Al-Hasawi on Wednesday and the npower Championship club are expected to make an announcement within the next 24 hours.
The 48-year-old Scot was dismissed by the Reds' old regime in June 2011.
After steering the club away from relegation following his appointment in January 2009 and then masterminding successive play-off campaigns during his first spell at the City Ground, Davies is on record as stating that he has "unfinished business" at the club.
Davies remains popular among Forest fans and the Al-Hasawi family, the club's Kuwaiti owners, are keen to win over supporters following the turbulent start to their tenure.
The Al-Hasawis are making their third managerial appointment since completing their takeover in the summer.
They began by sacking Steve Cotterill, who had just saved the club from relegation, within days of their arrival.
Sean O'Driscoll, who coached under former boss Steve McClaren, was brought back as number one but sacked on Boxing Day after a 4-2 home win over Leeds which left the Reds just one point adrift of the play-off places.
The surprising decision to sack O'Driscoll was followed by the Kuwaiti's stating their intent to appoint a manager with Premier League experience.
Former Birmingham and Aston Villa boss Alex McLeish was hired the next day but the Scot, after a brief 40-day tenure, left on Tuesday amid rumours of interference in team affairs from the owners.