Another three points would take them into the Premier League‘s top four before Liverpool face Manchester City on Sunday.
Jesse Lingard was handed his debut at Aston Villa in midweek and shone with two goals, combining well with Michail Antonio and Said Benrahma going forward.
Ryan Fredericks was brought back into the side to help shackle Jack Grealish, but Jarrod Bowen will be confident of having his place back at Craven Cottage.
With more than half the season gone, the Hammers are well placed in the race for Europe, but Moyes is still calling for more from his side.
Asked what the Hammers need to do to stay the course, the Scot said: “Same form, consistency, not too many injuries. All those things play a part and you need a bit of good fortune as well. We can do more, the players haven’t reached where they can get to.”
Predicted XI: Fabianski; Coufal, Dawson, Ogbonna, Cresswell; Rice, Soucek; Bowen, Lingard, Benrahma; Antonio
Saturday 5.30pm, Sky Sports
West Ham squad from: Fabianski, Martin, Randolph, Diop, Ogbonna, Dawson, Alves, Balbuena, Fredericks, Coufal, Johnson, Cresswell, Noble, Rice, Soucek, Fornals, Lanzini, Yarmolenko, Lingard, Benrahma, Bowen, Antonio, Odubeko