The Colombia international, on a two-season loan at Atalanta with an option to purchase, was once on the Hammers’ radar, but work permit issues saw a deal fall through.
Zapata finished as the second highest goalscorer in the Serie A last term after netting 23 goals – two more than Juventus’ Cristiano Ronaldo.
The 28-year-old definitely can fire West Ham to Europe at the end of next season, and many supporters want manager Manuel Pellegrini to bring him to the London Stadium.