The United boss has said the Argentinian pair, who have not played this season, will not have their contracts extended beyond the summer and are both looking for moves away from Old Trafford.
"Both of them have contracts until the summer and they're not going to be extended," Solskjaer said. "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 he's back now. They're professionals and they're working hard."
Speaking at a news conference on Friday, Solskjaer confirmed that winger Facundo Pellistri has tested positive for COVID-19 and will miss the chance to make his senior debut against Watford in the FA Cup third round on Saturday.
Odion Ighalo, who is likely to leave the club when his loan expires at the end of the month, could face his former club.
"Odion, it's special for him against Watford and he will be involved, he's in the squad," Solskjaer said. "He's been training really well.
"It's difficult for him to be out of the squad as many times because he did really well up until the summer. This season he's not had as many opportunities but he has not let himself down as a professional and a human being."
United begin their FA Cup campaign against Watford after reaching the semifinals last season. Solskjaer's team are well-placed in the Premier League and could go top of the table with victory at Burnley on Tuesday but the Norwegian said he will not throw away the chance to win the FA Cup.
"We enter this competition wanting to win," Solskjaer said. "There are a few players that had a few knocks and there will be a few changes but we'll still field a team I'm confident in."