The midfielder currently plays for Polonia Warsaw and has been linked with a season-long loan move to the City Ground.
Blackburn and West Brom have held an interest in the 22-year-old in the past, and Davies admits he is keeping tabs on Majewski.
"He is a player we have been looking at for quite a while, we know all about him and his international background and what have you," Davies told the Nottingham Evening Post.
"We will see what happens."
Davies is hoping to add to his squad before the start of the season, with a full-back seemingly the priority after Chris Gunter and Dan Fox were linked with moves.
He added: "We are short in one or two areas still and we do have plenty of work to do.
"There is no doubt about it, because we have players in the team who we do not want to fill those positions.
"We have to bring in players who can fill those gaps. We need the right people to play in the right areas.
"We hope to conclude one or two new signings over the next few weeks. Time is of the essence over the next week or so."
Coca Cola Ch'ship Promotion 09/10 Win Outright: Nott'm Forest 10/1