The Hammers will face a trip to either Liverpool or Manchester United should they get past Darren Moore's side on Saturday.
Moyes named a strong side at Stockport in the third round and has the chance to do so again against Doncaster.
Captain Mark Noble is expected to start while Fabian Balbuena and Issa Diop should get a chance at the back.
Michail Antonio is back fit but the Hammers must manage him carefully as the only senior striker, though Moyes has suggested more minutes might be exactly what he needs.
"There is a part of Mickey Antonio that needs a rhythm," said Moyes. "If you look at his best form, quite often I use the word rusty for him. He's rusty at the start and then gets going. We want to keep Mickey going.
"We gave him 20 minutes at Southampton, then 30 minutes and now we've got him to 90, maybe a bit longer than we would have wanted in some games, but I think it is the way to get Mickey back to full fitness."
West Ham predicted XI: Randolph; Fredericks, Balbuena, Diop, Johnson; Noble, Rice; Yarmolenko, Lanzini, Benrahma; Antonio
Saturday 3pm, BBC iPlayer/Red Button/BBC Sport Website
Venue: London Stadium
Referee: Robert Jones
West Ham squad from: Fabianski, Randolph, Martin,, Diop, Ogbonna, Dawson, Alves, Balbuena, Fredericks, Coufal, Johnson, Cresswell, Noble, Rice, Soucek, Fornals, Lanzini, Yarmolenko, Benrahma, Bowen, Antonio.
Injured: Masuaku (knee)