The 25-year-old striker is expected to see his first-team opportunities further limited by the arrival of Gonzalo Higuain, while Slaven Bilic is keen to sign another forward.
West Ham has identified Juventus forward Simone Zaza as its favored replacement for Andre Ayew.
The Ghana international lasted just 35 minutes of the Hammers' opening Premier League match against Chelsea before suffering a thigh injury.
He is now expected to miss up to four months of action, and despite the loan signing of Jonathan Calleri, Slaven Bilic would like to add another striker to his ranks.
Zaza, meanwhile, must contend with the arrival of Gonzalo Higuain at Juventus.