West Ham squandered a 2-0 lead at Crystal Palace in their last outing a week ago, wasting the momentum gained from a valuable 3-2 win over Tottenham Hotspur in the Carabao Cup days earlier - a game in which they won from 2-0 down.
But their form in the league sees them sitting 16th, a single point above the bottom three, having lost five of their 10 games thus far - including a 3-0 embarrassment at the hands of Brighton & Hove Albion in their last home game.
Meanwhile two of Liverpool's four draws and both of their two defeats have come away from home, though they have responded well to their 4-1 humbling at Spurs in the league a fortnight ago with their successive triumphs at Anfield.
But Liverpool's last truly convincing away performance came away against the Hammers back in May, thrashing Bilić's charges 4-0 thanks to Philippe Coutinho's inspired display in central midfield.
Though at such an early stage of the campaign, Jürgen Klopp's side will hope to produce a similar performance this weekend given they can hardly afford to fall further behind the top-six - a 12-point gap already separating them and first-placed Manchester City while Chelsea are three points ahead in fourth.
Having not won back-to-back league games since a demolition of Arsenal followed a narrow win over Crystal Palace at the end of August, this game is almost as much of a must-win as it is for the hosts.
Yet it is undoubtedly Bilić who is feeling the most pressure of the two managers. If West Ham were to lose they would be left on nine points after 11 league games - their worst total since 2010-11, when they were relegated to the Championship.
Both of their league wins have come on home soil this season and the Croatian boss has himself acknowledged the "need" for his side to claim "something" against their Merseyside visitors.
With ex-Crystal Palace manager Frank de Boer, former Everton boss Ronald Koeman and Craig Shakespeare - previously at Leicester City - all having been sacked already this season, Bilić is among the favourites next to go.
Concerns continue to grow as they struggle to put a consistent run of positive performances, and results, together and a win against a talented, if defensively-flawed, Liverpool side would provide another major - and much-needed - boost.
And given the away side's need for three points to inject fresh belief into their hopes of consolidating last season's Champions League qualification with another top-four finish this term, this clash appears to have intriguing repercussions whatever the outcome.
West Ham have been dealt a whole host of injury setbacks within the last week but centre-back Winston Reid and left-back Aaron Cresswell have been declared fit after a calf injury and a dead leg.
Right-back Pablo Zabaleta serves a suspension for accumulating five yellow cards while his deputy Sam Byram is out for at least a month with a muscle injury picked up in training.
Michail Antonio - who also slotted into the position - misses out with a rib injury and is not expected to return until later this month.
Defenders José Fonte and James Collins miss out with foot problems.
Liverpool will be without playmaker Coutinho for the third successive game but could welcome back winger Sadio Mané for a surprise cameo off the bench.
Coutinho has yet to shake off an adductor problem that has kept him out since Spurs while Mané - who hasn't featured since October 1 due to a hamstring injury - returned to full training on Thursday.
Liverpool will hope to have Dejan Lovren (thigh) and Georginio Wijnaldum (ankle) to call upon despite the duo picking up knocks against Huddersfield and Maribor respectively.
Adam Lallana (thigh) and Nathaniel Clyne (back) remain injured though the former could return after the forthcoming international break.
Recent form (all competitions)
West Ham United: WDLWD
Crystal Palace 2-2 West Ham United (Hernández, Ayew)
Liverpool 3-0 NK Maribor (Salah, Can, Sturridge)
These two teams have not played out a Premier League draw since December 2001 - with Liverpool winning eight and West Ham four of their 12 meetings since then.
The Reds have lost three of their last six league games against the West London outfit, as many defeats as in their previous 25 encounters.
Liverpool's only previous visit to the London Stadium saw them win 4-0 in May, their biggest away win over West Ham in the Premier League era and their best league win at the Hammers since January 1976.
All 41 of Javier Hernández's Premier League goals have come from inside the box, a record second only to Tim Cahill - who managed all 56 of his efforts for Everton from inside the area.
Seven of West Ham's nine Premier League wins at the London Stadium have seen them achieve 1-0 victories.
On-loan Hammers goalkeeper Joe Hart has conceded 29 goals in 17 Premier League games against Liverpool during his career. That is five more than he has let in against any other side.
Of the 16 goals that Liverpool have conceded this season, 15 have come away from home - the worst total of any team in the top-flight.
Liverpool have not conceded so many goals away from home in their first five fixtures since 1953-54, when they were relegated.
Daniel Sturridge has five goals in seven career league appearances against West Ham and needs two more goals to become only the seventh player to reach 50 Premier League goals for Liverpool.
Neil Swarbrick is the man in the middle for Saturday evening's game, the 51-year-old overseeing his eighth Premier League contest of the season.
The Lancashire FA official - a member of the Select Group of Referees since 2011 - oversaw West Ham's 3-0 defeat at Newcastle United in August but has yet to referee a Liverpool game this term.
He has dished out 22 yellow cards and no red cards across eight Premier League and EFL Cup games this season.