Zaza, who infamously missed a penalty for Italy in the Euro 2016 shoot-out with Germany, will arrive in east London having agreed personal terms with the Hammers. The move is likely to be an initial loan deal with the option to make it permanent at the end of the season.
Slaven Bilic told a press conference on Friday morning: "With the Zaza situation, it looks very likely to happen and should happen today,
"As far as I know, the deal is agreed between the clubs. The personal terms are also agreed and he is due in London today, so we hope it will be done.
"It's very positive and it's a boost. We've been trying for a long time now to get a top-quality striker and he was always mentioned."
The announcement of Zaza's imminent arrival follows confirmation of the arrival of Swiss midfielder Edimilson Fernandes. The 20-year-old has signed a four-year contract from FC Sion and was unveiled on Thursday evening.
Bilic does not anticipate any more incoming deals following Zaza's arrival but says either Reece Burke or Reece Oxford will leave the club on loan.
"Probably one or two of the young players will go out on loan, now we are out of Europe. [Martin] Samuelson and [Josh] Cullen have already gone. Oxford or Burke, one of them will probably stay here with us and one will go on loan."
On Thursday, West Ham crashed out of the Europa League before the group stages of the competition. Bilic's side suffered a 2-1 aggregate defeat to Astra Giurgiu for the second season in succession.