The Newcastle United midfielder, who is surplus to requirements at St James' Park, spent the second half of last season on loan at the City Ground.
Forest reportedly still have to agree a fee and come to an agreement on wages with Colback believed to be on around £40,000 a week.
Reds boss Aitor Karanka has admitted that Forest are ready to move on to other targets if a deal for Colback cannot be reached, the Spaniard keen to put the final pieces in place in his squad as soon as possible.
"I know Jack and Jack knows me and the club," Karanka told the Nottingham Post. "He was really important here last season.
"It is true that he is on our list. We have other players on the list, because he is not our player and we cannot say that he is yet. We have to find a solution to that as soon as possible.
"But if it is not Jack, then we will find another target. We are working to bring in another one or two. It depends.
"Now we know that we are an attractive team to come to. The main thing and the thing I want to have is the squad together as soon as possible."
The Sunderland academy product has one year remaining on his contract on Tyneside.