The Hammers also explored the possibility of signing Jamie Vardy from Leicester City prior to the striker signing a new contract, and have now turned their attentions to the versatile Ayew, who can play on the wing and through the middle.
Sources have told Goal that the Hammers have matched Swansea’s £20m valuation of the 26-year-old over the last 24 hours, after opting against haggling with their Premier League counterparts.
However, Swansea are yet to respond to the offer, with the Welsh club set to be without a recognised striker ahead of the new season should Ayew leave.
Nevertheless, personal terms are believed to have been agreed with the forward, and the club are hopeful of completing a deal in the next week.
Bafetimbi Gomis was loaned to Marseille earlier this week and the Swans have subsequently been linked with a bid for Sevilla forward Fernando Llorente.
West Ham, who could sell Diafra Sakho to West Brom this summer should the deal for Ayew be confirmed, are also set to confirm the loan signing of Argentina Under-23 striker Jonathan Calleri this week.