The 28-year-old has reportedly attracted interest from La Liga duo Barcelona and Atletico Madrid, with Serie A champions Inter Milan having already held talks regarding the centre-backs future.
However, Romero, who still has three years on his current Spurs deal, is thought to be preferring a move to La Liga this summer after a disappointing 2025/26 season.
The Argentine has played a crucial part in the heart of his nation's FIFA World Cup 2026 campaign, playing in six of the seven matches to reach the final against Spain on Sunday.
He joined the North London side in 2021 from Serie A club Atalanta, becoming an important part of the squad, making 156 appearances, scoring 13 goals and providing seven assists.
Tottenham are expected to demand a fee of around £50million for Romero, who missed the end of their relegation threatened campaign through injury.
Spurs manager Roberto De Zerbi has already strengthened his backline with the acquisitions of Netherlands defender Jan Paul van Hecke and Argentina's Marcos Senesi ahead of the new season.