Both Antonio and teammate Andy Carroll, who is also on the sidelines with a long-term injury, were left out of the squad for pre-season tours of Austria and Germany.
"Michail and Andy are in London," Bilic told reporters during the club's pre-season trip to Germany.
"He (Antonio) is ahead of the plan. The plan is for him to miss the first game of the season."
Bilic was less optimistic about injury-prone striker Carroll, who has featured only 12 times for the club in 2017.
The 28-year-old England international endured a stop-start campaign, nursing groin and knee issues for the majority of last season.
"Andy is still not able to train with the team but he is working hard at Rush Green with the physios," Bilic added.
"I am frustrated he cannot play, now he is still injured and it is a big loss for us."
West Ham meet Werder Bremen in a pre-season friendly on Friday before facing the German side again on Saturday.
(Reporting by Hardik Vyas in Bengaluru; editing by Sudipto Ganguly)
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