The 21-year-old midfielder was a standout performer for Denmark at Euro 2020, scoring two goals in five appearances, including a stunning free kick against England in the semi-finals.
Sampdoria are aware of interest in the midfielder and are willing to accept any offers in the region on £30m.
The Italian outfit only signed Damsgaard from Danish side FC Nordsjaelland in July 2020 for around £5.7m, but his sale this summer could help enhance their transfer budget.
Damsgaard, who has three years remaining on his contract, made 35 Serie A appearances last season, scoring two goals and providing four assists. body check tags ::