West Ham forward Michail Antonio is waiting to discover the extent of the hamstring injury which forced him off just seven minutes into Tuesday's Carabao Cup win over Newport.
Javier Hernandez, having missed the last two matches, is back in training after a knock to his knee and could return to face promoted Norwich on Saturday.
After spending nearly 18 months on the sidelines, Winston Reid is only a few weeks away from a potential return to full fitness.
Zimmermann was taken off in the midweek Carabao Cup clash with Crawley due to hip and back complaints while Drmic is back after a hamstring injury.
Grant Hanley has a groin injury which rules him out, though, and Timm Klose has a knee injury which could keep him sidelined for several months.
West Ham provisional squad: Fabianski, Balbuena, Fredericks, Diop, Ogbonna, Masuaku, Rice, Yarmolenko, Lanzini, Felipe Anderson, Fornals, Haller, Hernandez, Wilshire, Ajeti, Zabaleta.
Norwich provisional squad: Krul, Fahrmann, Aarons, Zimmermann, Byram, Godfrey, Lewis, Roberts, Vrancic, Leitner, Amadou, Tettey, Thompson, Pukki, Drmic, Srbeny