The Aston Villa defender made nine appearances for the Reds last term before ending the season on loan at Fulham, and Davies is keen to sort out a deal with the 29-year-old.
But the Forest chief is not interested in signing Mark Reynolds from Motherwell despite their manager, Craig Brown, saying a move to the Championship club would benefit the defender.
Davies told the Nottingham Evening Post: "It would be a no brainer for us to look at Nicky if he was available. If he is somebody we could possibly sign, then we have to look at it.
"He is a player with obvious quality and there is no question he did a good job for us while he was here. He would be a good addition if it could be done."
On Reynolds, he added: "I have spoken to Craig to clarify that he is not somebody we are interested in. He may be a decent player, but he is not on our list of targets."