While Fullkrug is still recovering from a long-term Achilles injury that has kept him sidelined since early-September, Kudus is serving the second of a three-game suspension that could be extended to a five or six-match ban if reports are to be believed.
Julen Lopetegui steered his side to an important 2-1 home win over Manchester United last weekend and made the bold decision to start Lukasz Fabianski in goal ahead of first-choice Alphonse Areola, who will be hoping to force his way back into the first XI this weekend.
Fabianski could retain his place between the sticks, though, while Jean-Clair Todibo will battle with Konstantinos Mavropanos for a start in a back four alongside Aaron Wan-Bissaka, Max Kilman and Emerson Palmieri.
Edeson Alvarez and Guido Rodriguez both started in midfield last time out, but one of those could be replaced by Tomas Soucek this weekend, unless the Czech comes in for Carlos Soler which would allow Lucas Paqueta to move over to the left side of attack.
However, Paqueta could continue in the number 10 role instead, and Lopetegui may decide to recall Crysensio Summerville, who scored his first Hammers goal last weekend, while Jarrod Bowen and Michail Antonio are set to retain their places in the final third.
West Ham United possible starting lineup: Areola; Wan-Bissaka, Todibo, Kilman, Emerson; Alvarez, Soucek; Bowen, Paqueta, Summerville; Antonio