Tottenham Hotspur are currently in line to win the race for the Argentina international, who is said to have agreed terms with the Premier League outfit.
However, according to Sportitalia, Barcelona have expressed an interest in signing the 23-year-old this summer.
As it stands, any deal appears highly unlikely with the Catalan giants being required to make multiple sales to facilitate a new contract for Lionel Messi.
With Romero said to be valued in the region of £50m, Barcelona would also realistically have to sell one of their most prized assets.
A transfer may become possible if Atalanta take an interest in members of Ronald Koeman's first-team squad who could be used in part-exchange.