West Ham summer signing Andre Ayew and striker Andy Carroll are still unavailable for Saturday’s clash at Crystal Palace.
Ghana hitman Ayew joined the Hammers from Swansea in August for a club-record £20.5m.
But the 26-year-old broke down with a thigh injury during his league debut and has been sidelined since mid-August.
Former Liverpool and Newcastle frontman Carroll, meanwhile, played four games at the start of the 2016/17 campaign before sustaining a knee injury.
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Bilic says both players are making progress in their bids to return to action.
He said: “Andre and Andy are still not fit but they are getting closer.”
In better news for West Ham, who went into the international break in the relegation zone, defender Aaron Creswell is ready to return this weekend.
The left-back is yet to feature this season after suffering an injury during a pre-season fixture.
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