The 22-year-old came through the youth ranks at Nordsjaelland before moving to Bologna in 2019, prior to which he was linked with a switch to Spurs.
Skov Olsen spent two and a half years on the books with the Serie A side, posting just three goals and five assists in 71 outings before joining Club Brugge in January.
The Denmark international has reignited his career with a respectable set of numbers in Belgium, recording 14 goals and 13 assists in 38 appearances and winning the Jupiler Pro League in his debut season.
Skov Olsen has continued his impressive form in the 2022-23 campaign, registering eight goals and four assists in 21 outings for Carl Hoefkens's men in all tournaments.
The attacker started four Champions League group stage games as Club Brugge sealed a historic last-16 place, scoring in a 4-0 win over Porto, and his form earned him a spot in Denmark's World Cup squad.
According to Belgian news outlet Nieuwslbad - via TEAMTalk - Tottenham are set to monitor Skov Olsen's performances in Qatar with a view to potentially moving for the youngster in January.
Skov Olsen started Denmark's opening game of World Cup Group D against Tunisia, but he only lasted 65 minutes of that goalless draw before being taken off by Kasper Hjulmand.
Skov Olsen was then left on the bench for Saturday's 2-1 defeat to defending champions France, but he still boasts a respectable record of eight goals and six assists in 24 caps for Denmark.
However, Club Brugge are in a strong negotiating position, as the former Bologna attacker is under contract with the Belgian champions until the summer of 2026.
Tottenham's attack has been decimated by injuries throughout the 2022-23 season, with Dejan Kulusevski missing a good chunk of the autumn period after picking up a hamstring injury in September.
Lucas Moura has also been dealing with a long-standing tendon problem, while Richarlison missed a few weeks of action with a calf injury that he picked up against former club Everton.
Son Heung-min sustained a nasty facial fracture in the Lilywhites' Champions League last 16-clinching win over Marseille in October, but he recovered in time to represent South Korea at the World Cup.
Ivan Perisic and Bryan Gil have provided alternative attacking options for Antonio Conte, although the latter is yet to start a Premier League game for the Lilywhites.
As well as a new forward, Tottenham could also look to move for a new creative midfielder, right-wing back and ball-playing centre-back when the January market opens for business.