A run of just one win in Everton's last nine games in all competitions has seen the pressure increase on Roberto Martinez, with speculation mounting over his future.
The Spaniard is having to cope with some key absentees, too, with goalkeeper Tim Howard sidelined by a calf issue, while defenders John Stones and Phil Jagielka are out with ankle complaints.
Martinez could well recall Romelu Lukaku and Samuel Eto'o as he looks to arrest a run of four successive defeats, but Antolin Alcaraz is out through suspension.
"I do feel that it is a game in which he have to perform well and have to win," the manager said.
"It will be a fantastic game of football and from our point of view it probably will be the start of something and give us a really good platform for the second half of the season."
The FA Cup certainly carries plenty of importance in the mind of Martinez, who guided Wigan Athletic to an unlikely triumph in his last season at the helm in 2013.
He added: "The FA Cup is the best cup competition in world football in terms of a domestic tournament and we look forward to it.
"It is a good time, not to experiment because it is not a word that I like, but to open competition for the players and do it in a different tournament.
"We are playing at home and against a very good side who will come with an open approach."
While West Ham's form has been far from as dispiriting as Everton's, Sam Allardyce will be keen for his men to bounce back from a run of three games without a win.
The boss is expected to shuffle his pack, with James Tomkins back available having served a one-game suspension for picking up five yellow cards.
Allardyce is significantly hampered, though, by the likely absences of key trio Alex Song, Diafra Sakho and Cheikhou Kouyate due to their involvement in the Africa Cup of Nations.
The sides have already met at Goodison Park this season, Lukaku and Leon Osman netting to earn Everton a 2-1 Premier League win.
The last FA Cup meeting between the two came in the 1990-91 quarter-finals, when West Ham triumphed 2-1.
