West Ham are relatively safe as they sit 12th in the table and nine points above the relegation zone, but the club's owners have called on Bilic to improve both performances and results.
The Hammers lost 3-2 at home to champions Leicester before the international break to heap more pressure on their under-fire manager, and only a top-half finish is likely to see Bilic avoid a potential summer exit.
Hull lost to Everton 4-0 last time out - a scoreline massaged by their late collapse after Tom Huddlestone's red card - but Marco Silva's Tigers will be in an unforgiving mood at the KCOM Stadium as they seek the points needed to keep themselves in the top flight.
Scroll down for Standard Sport's comprehensive preview....
Hull host West Ham with kick-off scheduled for 3pm on Saturday, April 1.
TV AND LIVE ONLINE COVERAGE
The match will not be televised in the UK. Standard Sport will bring you all the goals as they happen via Twitter, with a full report and reaction following the result.
West Ham are without Michail Antonio, Winston Reid and Pedro Obiang for the trip to Hull.
Winger Antonio is close to recovering from a hamstring problem but will not be ready, defender Reid is out a month with a thigh injury and midfielder Obiang will miss the rest of the season after undergoing ankle surgery during the international break.
But skipper Mark Noble is poised to return to the squad after missing the defeat by Leicester a fortnight ago with a dead leg.
Provisional squad: Adrian, Randolph, Byram, Fonte, Collins, Cresswell, Masuaku, Arbel
oa, Kouyate, Noble, Fernandes, Nordtveit, Snodgrass, Feghouli, Lanzini, Carroll, Fletcher, Calleri.
Hull skipper Michael Dawson could return to the squad for the home game against West Ham following a calf injury.
Centre-half Dawson, sidelined since early February, returned to full training on Wednesday and could be included in head coach Marco Silva's plans, but midfielder Tom Huddlestone starts a three-game ban.
Silva will make a late decision on whether to include striker Abel Hernandez, who only returned from international duty with Uruguay on Friday, while midfielder Evandro is still out due to a calf injury.
Provisional squad: Jakupovic, Marshall, Robertson, Maguire, Davies, Dawson, Ranocchia, Elabdellaoui, Elmohamady, Meyler, Henriksen, Grosicki , Hernandez, Diomande, N'Diaye, Clucas, Markovic, Maloney, Niasse.
Hull starting XI: Jakupovic, Elabdellaoui, Ranocchia, Dawson, Davies, Robertson, Markovic, Meyler, N'Diaye, Clucas, Hernandez
West Ham starting XI: Randolph, Byram, Fonte, Collins, Cresswell, Kouyate, Noble, Ayew, Lanzini, Snodgrass, Carroll
BETTING ODDS (via 888 Sport)
- Hull to win: 27/20
- West Ham to win: 43/20
- Draw: 47/20
Click here to place a bet. Odds correct as of April 1 at 9am.