The 23-year-old has been nursing a foot complaint in recent months, the same problem which saw him withdraw with England duty in March.
However, Rashford was passed fit for Thursday's first leg at Old Trafford, and lines up in attack with Paul Pogba, Bruno Fernandes and Edinson Cavani.
Solskjaer had kept schtum on who would be in goal for United, although David De Gea appears to have taken over as cup goalkeeper with Dean Henderson on the bench tonight.
Manchester United XI: De Gea; Wan-Bissaka, Lindelof, Maguire, Shaw; Fred, McTominay; Pogba, Fernandes, Rashford; Cavani
Subs: Grant, Henderson, Bailly, Mata, Greenwood, Amad, James, Telles, Matic, Williams, Tuanzebe, Van de Beek
Roma XI: Lopez; Smalling, Cristante, Ibanez; Karsdorp, Diawara, Veretout, Spinazzola; Pellegrini, Mkhitaryan; Dzeko
Subs: Mirante, Fuzato, Villar, Santon, Mayoral, Kumbulla, Carles Perez, Bruno Perez, Ciervo, Darboe
Man Utd squad from: David de Gea, Lee Grant, Dean Henderson, Nathan Bishop, Victor Lindelof, Eric Bailly, Phil Jones, Harry Maguire, Luke Shaw, Alex Telles, Aaron Wan-Bissaka, Brandon Williams, Axel Tuanzebe, Will Fish, Paul Pogba, Juan Mata, Fred, Bruno Fernandes, Amad Diallo, Daniel James, Nemanja Matic, Donny van de Beek, Scott McTominay, Ethan Galbraith, Shola Shoretire, Edinson Cavani, Anthony Martial, Marcus Rashford, Mason Greenwood, Anthony Elanga
Injury list: Martial (knee), Jones (knee)