Richarlison can be selected again after sitting out the Boxing Day win at Sheffield United under concussion protocol.
Rodriguez has missed the last five games in all competitions due to a calf problem.
The Toffees also have Lucas Digne (ankle) and Allan (hamstring) out of action, along with Fabian Delph (hamstring) and Jean-Philippe Gbamin (Achilles).
West Ham boss David Moyes must decide whether to risk Michail Antonio from the start.
Antonio came off the bench in the goalless draw at Southampton after a month out with a hamstring injury.
Fabian Balbuena will be assessed after missing out at St Mary’s while Arthur Masuaku is sidelined following knee surgery.
Everton (4-2-3-1): Pickford; Holgate, Mina, Keane, Godfrey; Doucoure, Davies; Iwobi, Sigurdsson, Richarlison; Calvert-Lewin
West Ham (4-2-3-1): Fabianski; Fredericks, Diop, Ogbonna, Cresswell; Rice, Soucek; Benrahma, Fornals, Bowen, Antonio
Everton squad from: Pickford, Olsen, Lossl, Kenny, Holgate, Keane, Mina, Nkounkou, Godfrey, Coleman, Branthwaite, Sigurdsson, Doucoure, Gomes, Davies, Richarlison, Calvert-Lewin, Tosun, Iwobi, Bernard, Gordon.
West Ham squad from: Fabianski, Coufal, Dawson, Diop, Ogbonna, Cresswell, Rice, Soucek, Bowen, Haller, Fornals, Randolph, Fredericks, Johnson, Balbuena, Noble, Snodgrass, Lanzini, Yarmolenko, Benrahma, Antonio.
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