The Red Devils had supposedly been hopeful of persuading the Serie A club to cash in on the centre-back for a bid of around £39m.
Romero starred on loan with Atalanta last season and La Dea have the option to purchase the Argentina international outright for £21.5m.
According to Tuttosport, Atalanta intend to trigger that right-to-buy clause and keep Romero at the Gewiss Stadium unless a big bid is tabled.
It is not believed that United have yet made an initial approach for the 23-year-old, who earned his first senior international cap in last week's 1-1 draw with Chile.
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