According to the Daily Star, the Whites have entered the race for his signature alongside West Ham, Southampton, and Tottenham Hotspur.
The 20-year-old is capable of operating anywhere across the midfield, and is often deployed as a winger by the Italian side.
The report goes onto state that Sampdoria have slapped a £15 million asking price on the Norwegian, who joined the club for just £5.2 million in the summer.
Claudio Ranieri, who is manager of the Serie A outfit and who won the Premier League with Leicester City, has claimed that the played is “very talented”, and his stats from this season are certainly impressive enough.
As per Wyscout, he has averaged a higher xG than Leeds man Mateusz Klich, as well making 1.86 more interceptions, and completing 12.2% more dribbles.
Marcelo Bielsa has set of a precedent for prioritising young, adaptable talent at Elland Road, and Damsgaard looks to fit the bill of his typical target down to the ground.
Elsewhere, financial guru Kieran Maguire has claimed that the Whites’ flying return to life in the Premier League could give them an edge over their rivals in the summer transfer window.
Leeds are currently 17 points clear of the relegation zone with 16 games left to play, and Maguire has told Football Insider that the closer and closer they get to their top flight status, the more it will allow Elland Road chiefs to make in-roads in the transfer market.
He said: “It will allow them to start making tentative enquiries with regards to player availability. Every club who is, for want of a better phrase, part of the ‘other 14’ has two budgets going forwards.
“One assuming they retain their position in the Premier League and another for if they are relegated. I think they can now scrap that second budget.
“Leeds are now in a position that if their name gets mentioned to a player or an agent, they’ll be saying ‘Well, I know I’d be playing in the Premier League next season.’
“That’s got to move Leeds ahead in the taxi rank."We’ve gathered the rest of this afternoon's Premier League gossip below:
1. Bielsa in court
Leeds United manager Marcelo Bielsa is up in court today as he looks to win a massive payout from former club Lille. The Argentine is looking for close to £17m in damages. (Get French Football News) (Photo by Stu Forster/Getty Images) Photo: Stu Forster
2. Leeds keen on Damsgaard
Leeds United are keen on signing Sampdoria midfielder Mikkel Damsgaard. Southampton, West Ham, and Tottenham are also interested. (Daily Star) (Photo by Alessandro Sabattini/Getty Images) Photo: Alessandro Sabattini
3. Leeds given transfer boost
Leeds United's strong position in the Premier League will given them an advantage over several of their rivals in the transfer market this summer, according to financial guru Kieran Maguire. (Football Insider) (Photo by Laurence Griffiths/Getty Images) Photo: Laurence Griffiths
4. Raiola talks about Pogba future
Paul Pogba's agent Mino Raiola has suggested that he will continue to 'work in the shadows' regarding the Manchester United midfielder's future. (TuttoMercatoWeb) (Photo by Michael Regan/Getty Images) Photo: Michael Regan