Sky Sports reports that the two clubs remain in active talks over the transfer, which would see the Argentine centre-back swap north London for the Metropolitano.
Bonus structures still need to be agreed, but negotiations are continuing without interruption as both sides look to find common ground on the final package, according to the broadcaster's reporting.
The move would also see Atlético see off competition from Inter Milan, who had been tracking Romero for much of the summer before Atlético's late surge pushed them ahead in the race.
Romero himself has made his preference clear, opting for a move to work under fellow Argentine Diego Simeone over the other options that had emerged, including Inter Milan and Arsenal — city rivals of Roberto De Zerbi's Tottenham.
Romero, who turns 28 this month, joined Tottenham from Atalanta in 2022 and has made well over 120 appearances for the club since, captaining the side to Europa League glory and picking up the competition's Player of the Season award along the way.
Spurs made him one of their key figures during that run, with performances at both ends of the pitch that established him as one of the Premier League's most combative and consistent defenders. His performances for Argentina at this year's World Cup, where he featured in all of his country's matches, only sharpened interest in his signature heading into the closing weeks of the European transfer window.
Both parties are said to be treating the coming hours as decisive, with an agreement on personal terms already believed to be in place between Romero and Atletico Madrid. Simeone is understood to have called Romero personally to discuss the move, with the defender coming away enthusiastic about the prospect of joining Atlético.
Should the fee be resolved, the Argentine could soon find himself lining up alongside compatriots Julián Álvarez, Rodrigo De Paul, Giuliano Simeone and Nahuel Molina in Madrid — assuming Atlético's own ongoing situation with Álvarez does not complicate the picture before the market closes.