Sky Sports report the Hammers and Roma are keen to sign the Argentine, but the forward is keen to stay with the Italian champions after returning to the club from loan spells at AC Milan and Chelsea last season.
London Stadium deal-makers are working hard to sign strikers after Marko Arnautovic, Andy Carroll and Lucas Perez all left the club this summer.
West Ham are already in advanced talks with Eintracht Frankfurt over the transfer of Sebastian Haller, while the club have also been offered the chance to sign Porto marksman Moussa Marega.
Higuain, 31, scored five goals in 18 games for Chelsea after moving to Stamford Bridge on loan for the second half of last season to be reunited with former Napoli coach Maurizio Sarri.
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The Blues opted against triggering their option to make the 31-year-old’s switch permanent and he has returned to the Old Lady where he will again work with Sarri.
However, Juventus have been linked with a move for Inter Milan striker Mauro Icardi, which has increased speculation over Higuain’s future.
Despite that, last month Higuain’s brother and agent, Nicolas, said the striker was determined to finish his career at Juventus.
“Gonzalo wants to respect his contract and therefore stay with Juventus for another two years,” he told Radio Marte. “His performances at Juve have been good and playing for another team in Italy isn’t a workable solution.
“I don’t want to disrespect anyone, but if Gonzalo plays in Italy again then he only will for Juve, who own him. I think this could be Gonzalo’s year. He has so much strength and determination, and he wants to end his career at Juve.”