Meanwhile, despite sitting top of the Championship standings, the Baggies make the trip to the London Stadium after a disappointing run of form in the second tier.
When David Moyes began his second West Ham reign with back-to-back wins, he would naturally have been optimistic about the rapid improvement of a squad which had underperformed for predecessor Manuel Pellegrini.
However, three games later and reality has set in for the Scot, who has witnessed his team fail to defeat Sheffield United, Everton and Leicester City.
While securing a draw with Everton last weekend was respectable enough, the performance during Wednesday's 4-1 defeat at Leicester would have set alarm bells ringing with Moyes, who will now feel that he has to make changes to his squad before the end of the month.
At a time when West Ham only remain out of the relegation zone on goal difference, a double-header with Liverpool and a trip to Manchester City feature in the club's next four Premier League games.
Despite holding the ambition to go far in the FA Cup, Moyes knows that Saturday's game is just as important in terms of building some confidence within the group before hosting the league leaders next week.
Belief has also been lacking at West Brom in recent weeks, with manager Slaven Bilic acknowledging that the Baggies have got themselves in something of a rut.
Nevertheless, on his return to a club who he has represented as a player and in the dugout, the Croatian will be expecting a response to Monday's home defeat to Stoke City.
The second-tier pacesetters are now six games with success in the Championship - a run of form which will concern Bilic ahead of their trip to Cardiff City next week.
For now though, Bilic can use this opportunity to hand game time to some of the fringe members of his squad - players who may become increasingly important during the closing months of the season.
West Ham FA Cup form form: W
West Ham form (all competitions): LWWLDL
West Brom FA Cup competition form: W
West Brom form (all competitions): DLDWDL
Having featured among the replacements at the King Power Stadium, Winston Reid could make his long-awaited playing return after a knee injury.
West Ham possible starting lineup:
Martin; Zabaleta, Reid, Balbuena, Masuaku; Sanchez, Noble; Antonio, Fornals, Lanzini; Ajeti
West Brom possible starting lineup:
Bond; Furlong, Ajayi, Bartley, Brunt; Barry, Livermore, Krovinovic; Edwards, Austin, Zohore
We say: West Ham 2-1 West Brom
Given their respective form and probable team changes, this match is a tricky one to call. However, while the Baggies may relish the chance to play at the London Stadium, we feel that West Ham will have just enough quality to edge through to the last 16.