The Hammers beat Swansea last weekend to pull eight points clear of the bottom three and will move to within a sniff of the 40-point mark with a second straight win.
Their hosts Sunderland are 10 points from safety with seven games to play, but David Moyes says his team will not concede defeat in their bid to beat the drop until it is mathematically certain.
"We've got a home game next, let's see if we can get some momentum, try to get a win in that and we'll try to do that," said Moyes.
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Sunderland host West Ham at the Stadium of Light, with kick-off scheduled for 3pm on Saturday, April 15.
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West Ham could be without Michail Antonio after the England international limped out of their narrow victory over Swansea on Saturday.
Bilic will also be unable to select Mark Noble, who picked up his 10th booking of the campaign against the Swans and will miss their next two fixtures.
Aaron Cresswell faces a fitness race as he bids to return from injury in time for the trip to Sunderland, Andy Carroll is expected to feature, but Winston Reid is out.
Sunderland will be without the suspended Sebastian Larsson, pending the result of their appeal, while Bryan Oviedo is out injured.
Sunderland City starting XI: Pickford, Jones, Kone, Denayer, Manquillo, Cattermole, N'Dong, Rodwell, Borini, Defoe, Anichebe
West Ham starting XI: Randolph, Byram, Fonte, Collins, Masuaku, Feghouli, Kouyate, Lanzini, Snodgrass, Ayew, Carroll
BETTING ODDS (via 888 Sport)
Sunderland to win: 23/10
West Ham to win: 6/5
Click here to place a bet. Odds correct as of April 10 at 4pm.