Sampdoria signed the young winger from FC Nordsjaelland last summer and he has made an impact in his first season in Italy.
He has already netted two goals and registered three assists in Serie A and has been attracting the envious glances of clubs across Europe.
His performances in Italy have piqued the interest of several clubs and Sampdoria could soon be tested with offers for the Dane.
Tottenham are amongst those clubs keen on Damsgaard, according to Italian journalist Nicolo Schira, with Jose Mourinho’s men having zeroed in on the winger as a talent.
It is unclear whether they have made any concrete move for the 20-year-old but the north London club are keeping an eye on him.
But they are not the only ones who are eyeing the young talent as it has been claimed that Bayer Leverkusen are also showing interest in Damsgaard.
Any clubs moving for the winger this month though are likely to be disappointed as it is claimed that Sampdoria do not want to think about selling Damsgaard before the summer.