The Argentina international quickly became a cornerstone of the Lilywhites' defence upon his arrival from Atalanta BC in 2021, initially joining on loan before signing permanently for £43.9m the next summer.
Romero has now made over a century of appearances for Tottenham, scoring seven goals and setting up one more, albeit while also receiving criticism for his rash and aggressive nature.
Nevertheless, the World Cup winner is thought to be admired by Real Madrid, who were tipped to move for a new centre-back in the summer transfer window but ultimately decided against it.
Carlo Ancelotti's side could try to move for a fresh face in defence in 2025, but according to Football Insider, Tottenham have no plans to let him depart and even want to agree a new deal with the defender.
Tottenham 'to sit down' with Romero and discuss new deal
Romero is not due to become a free agent until the summer of 2027, but the Lilywhites supposedly want to hold talks with the 26-year-old's entourage next summer to discuss fresh terms.
Romero recently caused a stir on social media, though, as he re-shared a post on X - formerly known as Twitter - from journalist Gaston Edul criticising Spurs' travel arrangements for international players after their 1-0 North London derby loss to Arsenal at the weekend.
"Tottenham lost to Arsenal again," the post read. "It does not end up consolidating itself to fight because it is not in the details. It was the only Premier League club that brought back its players from their national teams on its own and without its own logistics, as decided by its leaders. It gave it an advantage because its players arrived with less rest than the rest: Cuti Romero played with a feverish squad."
The Argentina international was partly to blame for the Gunners' winner, losing Gabriel Magalhaes at a corner before the Brazilian headed in the only goal of the game, although he quickly deleted the repost.
Either way, the report adds that Romero's social media activity does not indicate that he is unhappy at Tottenham, who are aware of the growing interest in his services and plan to extend his contract.
What did Ange Postecoglou say about Romero's repost?
Spurs head coach Ange Postecoglou was asked about Romero's controversial repost in Tuesday's press conference, as the Lilywhites prepare to travel to Coventry City for the third round of the EFL Cup on Wednesday.
The 59-year-old confirmed that he had been made aware of the incident, but he insisted that Romero was in the same boat as all other internationals coming back on Thursday and did not report any issues before the game.
"No, [the retweet] was mentioned to me but it wasn't mentioned to me before the game. I knew nothing about it. The players got back on Thursday and we had a Sunday game," Postecoglou said.
"No one reported anything other than the usual checks of people coming back from international duty so prior to the game - no one said anything. As I said, there was nothing before the game that was mentioned to me."
Romero could be rested for Wednesday's cup tie at Coventry, as Radu Dragusin and Ben Davies push for starts in the Tottenham backline, but Postecoglou confirmed that his side would be without a key midfielder for the trip.