Spurs are said to be weighing up an offer worth £45m from Brighton, with the 19-year-old keen to leave in search of regular first-team football.
Vuskovic is reportedly ready to hand in a formal request if necessary, with manager Roberto De Zerbi unable to guarantee him consistent minutes next season.
Tottenham have already added two centre-backs this summer, confirming deals for Marcos Senesi and Brighton's own Jan Paul van Hecke, as De Zerbi looks to add experience and leadership to a backline that conceded 57 goals last season. Andy Robertson has also arrived to strengthen the defence further.
Vuskovic enjoyed a productive loan spell at Bundesliga side Hamburg last season, performances that have attracted interest from clubs across Europe, including Bayern Munich and Barcelona.
The defender is using the World Cup as a platform to demonstrate his ability to potential suitors. He started as Croatia were beaten 4-2 by England in their opening group game and is expected to feature again when Croatia face Panama next week.
Vuskovic was signed by Tottenham from Hajduk Split as a 16-year-old in a deal worth around £12m, agreed in 2023 and completed once he turned 18 in 2025. He arrived with a reputation as one of the most promising young centre-backs in European football. His struggle to break into a settled first-choice pairing since then has frustrated both player and representatives, fuelling the growing sense that a transfer request may be the only way to force through a move this summer.
Asked about his future, Vuskovic said his focus for now remained on the tournament, while making clear his longer-term priority.
"For now I'm focused only on the World Cup," Vuskovic said. "My goal next season is to play for a club that wants me and where I will play. We'll see what happens in the coming days and weeks."