The 23-year-old centre-back is wanted at Tottenham, who have identified him as their top defensive target.
Fabio Paratici has been in talks with Atalanta to sign the centre-back, but for the moment there is no agreement between the two clubs.
Tottenham failed with an initial offer but the north London club are prepared to go in with a fresh bid to sign the Argentine.
According to Italian broadcaster Sportitalia, Tottenham are set to table a fresh bid worth €50m and put in another €5m based on add-ons.
Spurs are confident that they will be able to reach an agreement over a deal to take Romero to the Premier League.
The proposed offer is still short of the €60m fee Atalanta want before they agree to sell him this summer.
The Italian club are not under any financial duress to sell Romero and want to do a deal only on their terms.
Barcelona rate Romero highly, but are only in a position to sign him on an initial loan deal at present.