The 20-year-old winger joined Sampdoria last summer and has made an impact in his first season in Italy, scoring twice and registering four assists in Serie A.
His performances have piqued the interest of several clubs and he has already been linked with a move away from Sampdoria in the summer.
Tottenham are tracking the young winger and are claimed to be considering taking him to England when the window swings open again at the end of the season.
But they are likely to face stiff competition from one of the Italian heavyweights as, according to Turin-based Italian daily Tuttosport, Juventus are also keen on the Danish talent.
The Italian champions have been keeping tabs on Damsgaard and he is one of the player’s the club have identified as a potential target.
Inter and Bayer Leverkusen have also been credited with having an interest in Damsgaard ahead of the summer transfer window.
It has been claimed that more clubs are expected to join the race by the time the summer transfer window opens.
A value of €20m is mooted, but his price could rise over the next few months.
