West Ham are desperately searching for a striker with Andy Carroll and Andre Ayew both sidelined.
A short-term loan for Bony has been discussed, with the Ivory Coast striker expected to head to China in January.
But Italy international Zaza is also on their radar even though they face competition to sign him from Southampton.
Both clubs want the 25-year-old on loan with an option to buy but have been told that would cost £5m, with the purchase option set at £19m.
Reports in Italy suggest the Hammers also made an improved bid for AC Milan star Carlos Bacca this week.