The 30-year-old, who recently signed a new deal with the club, is back training on the grass in east London but their game against Brighton is likely to come too soon for the Hammers talisman.
Manager David Moyes remains keen to have the forward back as soon as possible, but will be wary of doing things too quickly and risking a third injury in quick succession after such a promising start to the season.
For their defeat to Chelsea on Monday, Moyes handed captain Mark Noble his first start since the opening game of the season to try and bring a bit more mettle to midfield. However, against a less threatening side in Brighton may be keen to bring Said Benrahma back into the fold from the off.
Predicted West Ham XI (4-3-3): Fabianski; Coufal, Diop, Ogbonna, Cresswell; Rice, Soucek; Bowen, Benrahma, Fornals; Haller
Sunday 2.15pm, Sky Sports
Last meeting: West Ham 3-3 Brighton
West Ham squad from: Fabianski, Randolph, Johnson, Coufal, Fredericks, Balbuena, Ogbonna, Diop, Cresswell, Rice, Soucek, Noble, Fornals, Benrahma, Bowen, Snodgrass, Lanzini, Yarmolenko, Haller.
Doubts: Antonio (hamstring)