The Hammers are known to be interested in Ayew, with reports claiming a bid was accepted last week.
It was thought the player was set to undergo a medical this week and be ready to play for the Hammers in their opening Premier League clash with Chelsea next Monday.
West Ham are yet to confirm the arrival of the 26-year-old forward, who only joined the Swans from Ligue 1 side Marseille last summer.
The Ghana international scored 12 goals in his debut season at Swansea, including one in each of his final three games of the Premier League campaign.
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