Central defence was always going to be the top priority for Tottenham this summer, and Romero has been identified as the club's No 1 target by transfer chief Fabio Paratici.
Reports from Italy claimed Spurs have already reached an agreement in principle with the 23-year-old, who impressed during Argentina's recent Copa America triumph.
Romero played the entirety of his country's 1-0 wins over Uruguay and Paraguay, before a knee injury ruled him out of the next three games - but he returned for the final as Argentina beat Brazil by a single goal.
His performances have put him on Barcelona's radar - but they may not be able to afford the defender as they look to tie his international team-mate Messi to a new deal.
Tottenham and Barcelona target Cristian Romero (Image: REUTERS)
Ronald Koeman's side have expressed an interest in Romero, according to Sportitalia.
But with the centre-back valued at around £50m, a deal looks unlikely - especially with Barca needing to offload players in order to facilitate a new long-term contract for their star man Messi.
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In the meantime, Tottenham will hope they can fend off competition from Barca and reach an agreement with Atalanta over a fee for their top target.
Football director Paratici is well aware of Romero's qualities, having previously signed him for Juventus.
According to journalist Gianluca Di Marzio, a deal is now edging closer as Spurs have an agreement in principle with the player over a five-year contract.
But the North London club are currently £6.8million (€8m) short of Atalanta's valuation of Romero.
Barcelona's interest in Romero could hinge on Lionel Messi (Image: EPA)
Negotiations remain ongoing and there is optimism a deal could be completed in a matter of days or weeks.
Should Spurs miss out on Romero, Paratici has a number of other targets lined up including Nikola Milenkovic of Fiorentina.
Other options include Takehiro Tomiyasu of Bologna, and Chelsea's Kurt Zouma.
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