West Ham boss Manuel Pellegrini said Arnautovic is in a race to get fit for Sunday's home match.
2018 ScheduleAll times ET
Jack Wilshere is facing a short period out after undergoing minor surgery on an ankle injury, West Ham's head of medical has confirmed.
West Ham summer signing Lucas Perez has hit back at "false" reports he refused to warm-up and come on as a substitute against Everton.
Andriy Yarmolenko scored two first-half goals as West Ham United defeated Everton 3-1 to claim their first Premier League victory of the season.
West Ham United manager Manuel Pellegrini said he remains confident in his team after a fourth consecutive defeat to start the season.
Adama Traore struck in stoppage time for Wolves as they beat bottom team West Ham to pile the pressure on Manuel Pellegrini's side.
Marko Arnautovic returned to training this week and will be ready as Manuel Pellegrini's side look for their first points against Wolverhampton.
The Chilean managed the Ivorian during his time at Manchester City and a reunion had been mooted after Yaya Toure left the Etihad this summer.
The centre-back endured a baptism of fire for West Ham United against Arsenal, but he has the qualities to be a Hammers cult hero.
West Ham United flirted with a potentially embarrassing League Cup second-round defeat by 10-man AFC Wimbledon before fighting back to win.
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