The Argentine pair have been told their contracts, which expire at the end of this season, will not be renewed and they are free to find new clubs.
Speaking ahead of his side’s FA Cup game against Watford this weekend, manager Ole Gunnar Solskjaer said: “Both of them have contracts until the summer and they’re not going to be extended.
“We’re looking for them to find clubs. Marcos has been given time to go home, so he’s still in Argentina.
“Sergio has been back home as well to see his family, but they’re professionals, working hard and ready if they are called on for us.
“Marcos will have to travel and do the quarantine before [if he rejoins the squad].”
Solskjaer admits Manchester City have more quality.
He is expected to move to Boca Juniors ahead of this summer’s Copa America.
Romero first joined United in 2015 but has never managed to establish himself as No.1 ahead of David de Gea.
He has made just one Premier League appearance over the past four seasons and with the return of Dean Henderson this summer his chances of first-team football were limited even further.
Rojo, meanwhile, joined in 2014, and despite being an important part of the first-team squad injuries have recently disrupted his United career.
He is yet to feature this season and looks to have played his final game for the club.
It is not clear where he could end up, but speculation has linked him with the likes of Newcastle United in recent times.