Roy Hodgson's side are long-term admirers of the 29-year-old Londoner and tried to sign him before, says the Mirror.
They were linked last summer but a move failed to materialise.
However, there is now a feeling they can get him after the Hammers strengthened their attack with Pablo Fornals and Sebastien Haller.
Palace face an uncertain couple of weeks before the transfer window closes with Wilfried Zaha's future still in the air.
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