Celtic are set to continue making additions in January, according to a report in the Daily Mail.
The Bhoys have already signed Erik Sviatchenk from Midtjylland in a deal that the Mail value at £1.5 million.
However, Ronny Deila is still not fully satisfied with his squad at Parkhead, and he wants to bring in Rasmus Falk from Odense.
Falk is out of contract at the end of the season, meaning that he could be available in a cut price deal.
The 24-year-old midfielder is also said to be of interest to French club Lille, but Celtic are apparently leading the race for his signature.
Odense only want £150,000 for Falk, and Deila believes that he could prove to be a bargain buy if he can seal a deal in the coming weeks.
Celtic are now in discussions with Odense, and hope to push through a move in the imminent future.
Falk has played 18 times for Odense this season in the Danish Premier League, and he has scored twice in the process.
He has also earned one cap for Denmark, although that did come back in 2013.