Spurs are keen to land Romero and football managing director Fabio Paratici has gone to work in negotiating a deal to take him to north London.
Tottenham have increased their bid from €43m plus bonuses to €50m plus bonuses, according to Italian outlet Tutto Mercato, and are confident that a deal can be done.
It is claimed that Atalanta coach Gasperini does not want to lose Romero, however he looks to be fighting a losing battle.
Gasperini is keen for Atalanta to bring in Merih Demiral from Juventus if he does lose Romero.
Spurs have agreed to sell Toby Alderweireld to Qatari side Al-Duhail and are pushing to add Romero to the ranks.
Romero clocked 31 appearances for Atalanta over the course of last season as he helped his side to finish third in Serie A and secure Champions League football.
He also turned out in the Champions League, playing against FC Midtjylland, Ajax, Liverpool and Real Madrid, as Atalanta reached the last 16.
