The talented Croatian has been linked with a move out of Spurs following an exceptional campaign on loan at Hamburg.
Vuskovic was one of the Bundesliga's standout defenders, and even bagged six goals from centre-back, with Brighton chasing his signature.
Only last week, the Seagulls had a £30 million bid rejected for the 19-year-old, and now BBC Sport has revealed the Premier League side have no "immediate plans" to launch a second offer for him.
In the meantime, Spurs have agreed a £52m deal to sign Brighton defender Jan Paul van Hecke, with Roberto De Zerbi at the forefront of negotiations.
Brighton are happy to pocket over £50m for a player whose contract expires in June 2027, while Tottenham are pleased to sign one of the best defenders in England's top-flight.
Van Hecke is now set to become Tottenham's third signing of the summer window after Andy Robertson and Marcos Senesi were captured on a free transfer.