Spurs’ new football managing director Fabio Paratici has zeroed in on the Argentina international as a centre-back option he wants to snap up.
Tottenham already have a deal in place for Atalanta’s Pierluigi Gollini and they want Romero from the same club.
According to Argentine outlet TyC Sport’s Cesar Luis Merlo, Tottenham are in advanced talks to sign Romero and are offering €40m plus €10m in bonus payments.
The Premier League side have a contract until 2026 ready for Romero to sign.
Romero further boosted his stock this summer when he helped Argentina to win the Copa America and landing him would be a coup for Tottenham.
Atalanta are keen to make sure they only accept a deal they are happy with for the defender though.
Tottenham are also closing in on Sevilla winger Bryan Gil, with Erik Lamela set to go the other way as part of the deal.