The Aston Villa defender made nine appearances for the Reds last term, and Davies is keen to sort out a deal with the 29-year-old.
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."