The Argentine goalkeeper, who joined United on a free transfer in July 2015, had started the Red Devils' first six games of the season as speculation mounted over David De Gea's future but he has made just one appearance since the Spaniard's failed move to Real Madrid.
And Goal understands that, while Romero is seen as a positive influence in the United dressing room, he could well be allowed to leave the club in the summer, even if De Gea does seal a switch to the Bernabeu.
Despite keeping four clean sheets in the games he played throughout August, Romero had his nervous moments in the United goal and was never seen as the ideal long-term replacement for the Spain international, who eventually returned to the starting XI for the 3-1 win over Liverpool.
READ MORE | The games Rooney will miss through injury
Goal has learned that Deportivo La Coruna goalkeeper German Lux is an alternative option for River, with current No.1 Marcelo Barovero set to leave the club in the summer after four years with Marcelo Gallardo's side.
Indeed, Lux revealed to Continental recently that he would be open to a return to the club. He said: "I would like to go back to River at some point. It is a dream I have. I learned my trade there, I had some great times and I have that idea in my head.
"I do not want to put myself forward for anything, less still do I know if this is the right time. Nobody knows that. I am trying to focus on this season and we will see afterwards."