Thomas Tuchel is searching for more reinforcements between the post after Argentine Willy Caballero, 39, was released in the summer.
According to The Telegraph, Caballero's country man Romero, also without a club, is emerging as a possibility.
He has been at united since 2015 and largely provided back up for long-time No1 David De Gea, 30.
He was due to join Everton on loan before the start of last campaign until united blocked the move the last minute.
After being completely outcasted from the Old Trafford setup, Romero spent much of last season away in Argentina.
He has since been linked with moves to Juventus, Everton again and now Chelsea.
The Blue moved for Edouard Mendy, 29, from Rennes last summer and the Senegal international replaced Kepa Arrizabalaga, 26, as No1.
Mendy kept 25 clean sheets in his 45 appearances, including one in the champions League final win against Manchester city.
Chelsea have been linked with a move for Middlesbrough's Marcus Bettinelli, 29, and Wayne Hennessey, 34, who instead joined Burnley.
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