Summer signing Bailly has not played since the harrowing 4-0 Premier League defeat to Chelsea in late October where he picked up the knee ligament injury that has kept him sidelined. The Ivory Coast international returned to training this week however as he edges closer to a return, but Sunday's trip to Goodison Park will come too soon for the 22-year-old.
Smalling meanwhile has also not played since that heavy defeat at Chelsea, with Phil Jones and Marcos Rojo stepping in to fill the void at the heart of defence.
Shaw was taken off at half-time during the comfortable EFL Cup quarter-final win over West Ham on Wednesday with Daley Blind coming onto replace him. The Netherlands international is likely to continue at left-back on Sunday with the former Southampton winger struggling with what Mourinho describes as a "little injury".
"The injury [to Luke] is a pity," Mourinho told United's official website. "We were on this process of developing him as a player – he has a lot to learn and great potential to develop so we were giving him 90 minutes. Not consecutive matches but 90 minutes against Feyenoord then, one week later, 90 minutes against West Ham, but he got this little injury.
"In the squad, we are in a very good position with injuries – the two central defenders and Luke is what we have. Everybody is doing really well to keep that record good in such a difficult season with so many matches. Hopefully, we progress in the cup competitions and have more cup games to play in the second part of the season."
Wayne Rooney will miss the trip to his former club having picked up his fifth booking of the season in that victory over West Ham. Paul Pogba and Marouane Fellaini however are both back in contention having served their respective suspensions in that cup victory.