Romero has been widely expected to leave Spurs this summer following back-to-back 17th-place Premier League finishes and a complete overhaul of the club's management structure under Roberto De Zerbi.
Barcelona and Atletico Madrid had been considered the frontrunners for his signature, but Manchester United's interest has now emerged as the most concrete domestic option.
The 28-year-old and Martínez have played together 17 times for Argentina and lost only once as a pair in the national team, forming a partnership that also contributed to Argentina's 2022 World Cup triumph in Qatar. That personal and professional familiarity is understood to appeal to both player and club.
United need to strengthen their defensive options ahead of their Champions League return next season. Manager Michael Carrick has made reinforcing the backline a priority alongside his midfield rebuilding programme. Romero's combination of intensity, aggression and quality in possession fits the profile.
Tottenham would demand a significant fee for a player who has been arguably their best performer over the past two seasons despite the club's broader struggles. The balance of negotiations will test both clubs' resolve before the window opens.