Moyes' side could only muster a 0-0 draw last time out, but will be expected to gain a place in the fourth round as they face Shrewsbury on home soil at the London Stadium this time around.
The east Londoners will come into the game in buoyant mood after disposing of relegation rivals Huddersfield away from home by four goals to one, thanks to strikes from Mark Noble, Marko Arnautovic and a brace from Manuel Lanzini.
However, they will be without strikers Andy Carroll and Javier Hernandez for the cup clash. Carroll misses out once again with Premier League rivals Chelsea said to be interested, while Hernandez is suffering from the flu.
The Mexican was sent home from training on Monday and it is likely that Arnautovic will remain in the side tasked with firing the Hammers into the next round at the expense of Paul Hirst's side.
Joe Hart is expected to face his old side again, while 24-year-old Sam Byram returned from a long-term groin injury with the Under-23's last week. He has managed just 270 minutes of first-team action this term, while Reece Burke, Declan Rice, Josh Cullen, Andre Ayew should all come in.
Reece Oxford could be given a start too after returning from his loan with Borussia Monchengladbach, with Moyes is expected to keep the same formation once again.