Spurs slipped to another Premier League defeat on Monday night (Tuesday AEST), their 18th of a poor domestic campaign, after a 2-1 loss at home to Nottingham Forest.
It occurred days after Ange Postecoglou's team progressed to the last four of the Europa League with an impressive 1-0 victory at Eintracht Frankfurt.
Romero starred in Germany, but has only played 23 times in an injury-hit season.
Recent reports in Spain have linked the World Cup winner with a move to Atletico Madrid.
In an interview with Argentinian journalists Esteban and Gaston Edul, the 26-year-old spoke about his future, with his contract at Tottenham set to expire in the summer of 2027.
Asked what new league he would like to play in, Romero said in Spanish: "I'd love to play in LaLiga. I'd love to, honestly.
"We'll see after the championship is over. The truth is, I haven't spoken to my agent yet, but I'm open to anything. My goal is always to grow and go to new places to continue developing.
"There are two months left until the end of the season and I'm always thinking about performing at my best.
"We're in the Europa League semi-finals. It's an important step for the club, which hasn't reached this stage for so many years. I'd like to win it."
Romero's comments are unlikely to go down well at Tottenham, who are 16th in the Premier League.
Postecoglou revealed the decision to withdraw Romero and his centre-back partner Micky van de Ven at halftime on Monday was "pre-planned", and explained why it was important for the duo to start.
"I thought they needed to play some minutes because it becomes 10 days leading into Liverpool (on Sunday),'' the Australian said.
"With both of them, we've got them in a really good place physically now and I just want to keep them ticking over. I felt that there was no need to play more than 45 minutes today and we needed to give a couple of others game time."
Postecoglou also revealed Destiny Udogie was rested and unused substitute James Maddison was "fine" after being forced off in Frankfurt.
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