The Norwegian is keen to trim down his squad as they aim to continue their unlikely Premier League title challenge, which could free up funds to bring in more active replacements.
Solskjaer has spoken about his plans for the January transfer window, and he mentioned those who are out of contract in the summer.
Having revealed that their time at the club will not be extended, he revealed that both Sergio Romero and Marcos Rojo could leave Old Trafford this month.
“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 in England now.
“But they’re professionals, they’re working hard and they’re ready if they’re called in for us. I’m sure they’re ready. Of course, Marcos will have to travel and quarantine before [playing again].”
Romero has slipped to third in the pecking order following the return of Dean Henderson, and looks unlikely to play again despite his fine record in goal.
The 33-year-old Argentina international has kept 39 clean sheets across 61 appearances for the club, with the vast majority coming in cup competitions.
Rojo, who returned on loan to Estudiantes earlier this year, looks set to return home on a permanent deal having fallen behind Eric Bailly, Victor Lindelof, Harry Maguire and Axel Tuanzebe in the pecking order.
Solskjaer said of Rojo last season: “Marcos is a lovely lad, he's got the fire in his belly, he's a winner and he wasn't getting enough football here.
“It was important for him to start playing. He wants to come back a fitter and better player, hopefully having played well for Estudiantes and helped Seba [Veron] and his club, and gone to the Copa America.
“So that was something we just had to do.”