Inter Milan are also continuing their search for a buyer for defender Benjamin Pavard.
Inter have identified Romero as their priority target to fill the gaps left by the departures of Francesco Acerbi and Stefan de Vrij, with talks accelerating after his representative arrived in the city at the same time as sporting director Piero Ausilio returned from Germany.
Tottenham are demanding a fee of around €50m for the World Cup finalist, a figure Inter consider high but are nonetheless working to bridge, potentially through a structure involving bonuses to make the deal more financially sustainable.
Romero, who previously played in Serie A for Genoa and Atalanta before his move to the Premier League, is understood to be open to a return to Italian football, with the prospect of competing for major honours at Inter seen as an added draw.
The Nerazzurri view the defender as an ideal profile to add international experience, personality and quality to their back line, and are concentrating much of their transfer efforts on getting the deal over the line, though the financial gap with Tottenham remains the chief obstacle, with Barcelona and Chelsea also credited with interest despite Inter having opened direct talks first. The coming days are expected to be decisive in determining whether Spurs will lower their valuation or hold firm.
Elsewhere in Inter's defensive business, Benjamin Pavard has emerged as a target for Saudi Arabian side Al-Ittihad following his return to the club after Marseille declined to trigger the buy option in his loan deal.
According to fussballeuropa.com, representatives for the Saudi club have made contact with Pavard's camp, with Inter hoping to recoup at least €20m for the French defender. Pavard, 30, remains under contract at Inter until 2028, though the club consider him surplus to requirements and are actively working to move him on before the transfer window closes at the start of September.
Pavard made 27 appearances for Marseille last season, but the Ligue 1 club ultimately opted against triggering the €15m option in his loan agreement, leaving his long-term future unresolved for a second successive summer.