The 28-year-old hit 28 goals for Serie A club Atalanta while on loan from Sampdoria, and is viewed by Manuel Pellegrini as a potential replacement for the departed Marko Arnautovic.
According to the report, any deal for Zapata would cost the Hammers around £40 million this summer.
This would be a fantastic signing. Zapata may not be the youngest player linked with West Ham this season at the age of 28, but he is a goalscorer, and it has been proven last season that if you out your faith in him and build a team around his image, he will carry a side with his strikes. 28 goals is some return, but that stat only really tells half the story. 3.2 shots per game and 1.8 key passes per match in the Serie A [Whoscored] last season hint at a player who is a well-rounded, creative force. £40 million isn’t cheap by any stretch, but the Irons need a danger man, and the longer their hunt for a striker goes on, the more expensive it is bound to be become. Snapping up Zapata sooner rather than later would, therefore, be a smart idea from the Hammers.