Spurs are set to do business with Atalanta by snapping up goalkeeper Pierluigi Gollini on a loan deal, with the player set to fly to England to complete the move.
The north London side want Gollini’s team-mate Romero too and are trying to put a deal in place to sign him.
However, according to Italian broadcaster Sportitalia, Tottenham have now seen Atalanta turn down two proposals for Romero.
Tottenham are continuing to push for the Argentina international, but Atalanta value him at €60m.
Spurs first enquired about Romero on 13th July and are moving quickly in their efforts to sign him.
They could yet face competition though as it is claimed Barcelona are keeping a close eye on the situation concerning the defender.
Romero is at the top of Barcelona’s shortlist of potential centre-back signings, but the Catalan side are trying to cut costs to balance the books.