Andre Ayew joined Swansea City from Olympique Marseille last season on a free transfer. The 26-year-old attacker kicked the ground running, winning the Barclays Player for the month of August and subsequently won the top scorer of the club in the English Premier League with 12 goals.
Ayew is now discussing personal terms with the Hammers.
Swansea hope to complete the signing of Atletico Madrid striker Borja Baston to add to the arrival of Spain forward Fernando Llorente from Sevilla.
Forwards Alberto Paloschi, Eder and Bafetimbi Gomis have already left Swansea this summer.
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Manager Francesco Guidolin admitted in July he was unsure about Ayew's future, but hoped he would stay.