The Ivory Coast international stayed overnight in hospital for checks, following a heavy collision with Harry Maguire, while Luke Shaw also remains sidelined with an ankle injury.
Solskjaer has also opted to keep faith in under-fire goalkeeper David de Gea, though Timothy Fosu-Mensah replaces Aaron Wan-Bissaka at right-back.
The United manager said of Bailly: “Eric stayed down in London for all the checks and he’s done all of them.
“I didn’t see him yesterday and he followed the protocols that are needed. I don’t think he’ll be ready for this game. I think everyone is available apart from that.”
Solskjaer mainly returns to the team that has performed so well since lockdown with Paul Pogba, Mason Greenwood and Anthony Martial all returning.
He wants a response after Sunday’s 3-1 defeat, which ended United’s 19-game unbeaten run and chance of a first final under the Norwegian.
“We’ve just got to stick together and stay strong,” he said. “We’ve got two games to go and we’ve given ourselves a good chance.
“When you lose a game you’re hurt and disappointed,” he added. “You’ve got to focus on the next thing. Defeat is not the end of the world. It was end of the FA Cup dream and a final, but it’s business as usual and onto the next game.
“We’ve had so many setbacks as a club, lost games before and now we have to put on a performance.
“I think we’ve grown over the whole season and the added pieces of Odion (Ighalo), Bruno (Fernandes) and Paul (Pogba) and Marcus (Rashford) coming back is a strength for us. We are better as a group, more robust and resilient.
“The proof is in the pudding and we’ll have to see on Wednesday how they’re going to perform.”
Man Utd XI: de Gea, Fosu-Mensah, Lindelof, Maguire, Williams, Pogba, Matic, Greenwood, Bruno Fernandes, Rashford, Martial
Subs: Mata, Lingard, Fred, Dalot, James, Romero, Ighalo, Wan Bissaka, McTominay
West Ham XI: Fabianski, Johnson, Diop, Ogbonna, Cresswell, Soucek, Rice, Bowen, Noble, Fornals, Antonio
Subs: Balbuena, Yarmolenko, Felipe Anderson, Lanzini, Wilshere, Haller, Masuaku, Randolph, Coventry
Referee: Paul Tierney