Konchesky, who joined Liverpool from Fulham in the summer, had been linked with a return to Craven Cottage but the move fell through after the Cottagers were unable to move on Mexico full-back Carlos Salcido.
Konchesky, 29, was signed on transfer deadline day in August by ousted Reds manager Roy Hodgson but immediately lost his place in the Liverpool side under new boss Dalglish, who prefers to play Glen Johnson out of position at left-back.
FIFA rules stipulate that no player can play for three different clubs in a single season and Konchesky has already played for both Fulham and Liverpool but the move is an emergency three month loan and as such the rules do not come into force.
Konchesky said: "There was talk of me going back to Fulham and it didn't happen. I could have sat at Liverpool and just done nothing but I want to play football. I wanted to come to a team that was fighting for promotion.
"They play good football here and I want to be part of it and trying to get the team in the Premier League.''
Admitting his dream move to Liverpool had not worked out, he added: "It was a tough start and then the manager that took me there got the sack and it was a big change.
"But that's part of life, I had to go to try it, it hasn't worked out, I want to get my football back on track, and I've been given an opportunity at Nottingham Forest.''
Meanwhile, Liverpool defender Daniel Ayala has been loaned to Derby County.