The 24-year-old Vitesse Arnhem star, has been heavily linked with a move to the Premier League, after a series of impressive performances in the Eredivisie this season.
Bony is currently 2012/13 top scorer in Holland, with 16 goals in just 18 appearances, and recently featured at the Africa Cup of Nations in South Africa.
Reds boss Brendan Rodgers had been credited with an interest in bringing Bony to Anfield, prior to the January arrival of Daniel Sturridge from Chelsea.
Upton Park chiefs fear the England international is determined either to prove himself at Anfield or rejoin old club Newcastle United instead of signing a £17million deal to stay in East London.
Signing Bony would prove to be an impressive transfer coup for West Ham, who will have to fight off widespread interest in the £12million-rated player's signature, given that he is one of the most promising strikers around at the moment.