The 26-year-old midfielder spent last season on loan at Chelsea, but made just eleven appearances for the club.
Chelsea have decided against exercising the option to buy him this summer, however he is expected to return to the Premier League ahead of next season.
The Hammers have identified Zakaria as a target and are set to press ahead with their efforts to sign him in the ongoing transfer window.
According to Italian outlet Tutto Mercato, the Hammers are likely to table a bid for the Juventus midfielder ahead of the weekend.
With Declan Rice’s transfer to Arsenal getting closer after West Ham received an offer in excess of £100m, the Hammers are keen to bring in reinforcements as soon as possible.
David Moyes admires Zakaria and the east London club are hoping to make headway in their pursuit of the Juventus midfielder in the coming days.
The Bianconeri are prepared to sell him and are waiting for an acceptable offer to land on their table.
The West Ham boss wants to sign two midfielders to replace Rice and Zakaria is expected to be one of them.