The 28-year-old appeared for his home nation in last summer’s World Cup Final, but is now a free agent after seeing out his contract with Sampdoria.
And reports claim that United are keen to offer him a quick route back into top-level football, with an agreement on the verge of being made official.
Romero is understood to have had a medical in the past few days, opening the door for an official announcement.
Any deal for the South American could see David de Gea or Victor Valdes leave, with the former wanted by Real Madrid and the latter thought to be available after public criticism from Louis van Gaal.
Romero signed for Sampdoria from AZ Alkmaar in 2011 when the Italian side were in Serie B.