The Hammers board have called on Bilic and his players to improve results in a bid for a top-half finish after Joshua King's hat-trick secured a last-gasp 3-2 win for Eddie Howe's Cherries on Saturday.
The match holds more significance for Leicester, who will go back to the reality of a relegation battle following their stunning progress to the Champions League quarter-finals with a midweek win against Sevilla.
Craig Shakespeare has won his first three games as manager following the sacking of Claudio Ranieri, but must keep his players focussed on survival with minds.
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West Ham host Leicester at London Stadium with kick-off scheduled for 3pm on Saturday, March 18.
The match will not be broadcast on UK television, but you can follow all the build-up and action from 2pm with Standard Sport’s London Football live blog. Enter your email address below to be informed when coverage begins.
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West Ham skipper Mark Noble is ruled out due to a dead leg.
Winston Reid will take over as captain while Sam Byram could be recalled at right-back, freeing up Cheikhou Kouyate to move into Noble's midfield berth.
Andre Ayew is set to start in attack after scoring as a substitute at Bournemouth last weekend, but defender Angelo Ogbonna (knee) and striker Diafra Sakho (back) are still out.
Provisional squad: Randolph, Adrian, Fonte, Reid, Collins, Byram, Cresswell, Masuaku, Kouyate, Nordtveit, Obiang, Quina, Antonio, Fernandes, Snodgrass, Feghouli, Lanzini, Carroll, Calleri, Ayew, Fletcher.
Leicester's January signing Molla Wague is out for the season with a dislocated shoulder.
The defender made just one appearance - in the FA Cup defeat at Millwall in January - and has had an operation but his long-term future is unknown, with the loan from Udinese expiring in the summer.
Nampalys Mendy is rated as 50-50 to return from a knee injury which saw him miss the 2-0 win over Sevilla on Tuesday and advance to the Champions League quarter finals 3-2 on aggregate.
Provisional squad: Schmeichel, Hamer, Zieler, Simpson, Huth, Morgan, Wasilewski, Chilwell, Fuchs, King, Mendy, Drinkwater, Amartey, Ndidi, Mahrez, Gray, Albrighton, Kapustka, Musa, Vardy, Okazaki, Ulloa, Slimani.
West Ham starting XI: Randolph, Kouyate, Fonte, Reid, Cresswell, Feghouli, Fernandes, Obiang, Lanzini, Antonio, Carroll
Leicester starting XI: Schmeichel, Simpson, Morgan, Huth, Fuchs, Mahrez, Ndidi, Drinkwater, Albrighton, Okazaki, Vardy
BETTING ODDS (via 888 Sport)
West Ham to win: 13/10
Leicester to win: 9/4
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Odds correct as of March 17 at 4pm.