According to a report from Italian media outlet Calciomercato (via HITC), Spurs managing director of football Fabio Paratici is very interested in agreeing on a deal with Sampdoria for the playmaker.
However, Spurs will face plenty of competition for his signature after his excellent displays for Denmark at Euro 2020, leading to him being tracked by the likes of Leicester City, West Ham United, Southampton, Crystal Palace and Leeds United during this transfer window.
The report adds that Damsgaard's representatives are in talks with several Premier League clubs about a potential move to the English top flight.
Given the current financial situations of several clubs, it is more likely that Damsgaard will leave Sampdoria for a Premier League club, with plenty of European clubs that are interested in him struggling financially.
The 21-year-old scored an outstanding goal in Denmark's Euro 2020 semi-final loss against England, nestling a freekick right into the top corner.
The Danish international moved to Sampdoria in a £5 million deal from Nordsjaelland last summer, and he managed two goals and four assists in 35 games in Serie A last season.
Reports indicate that Sampdoria will not allow the winger to leave for a transfer fee that is less than £34 million this summer, especially since he has a contract with the club until June 2024.