Arnautovic, who has scored twice in three Premier League matches this season, was substituted in the 59th minute of West Ham's 3-1 defeat at Arsenal last weekend.
The Austria international was not involved in the EFL Cup clash with AFC Wimbledon on Tuesday, meanwhile, and was seen as a doubt for Saturday's clash with Wolves.
However, Pellegrini has revealed that the 29-year-old is in contention to return to the XI against last season's Championship winners.
"Marco has a small problem behind his knee. In the last game [against Arsenal] he was not comfortable to play the final minutes, but he has had all the examinations with the doctor and worked the whole week," Pellegrini told reporters.
West Ham have lost all three of their Premier League matches at the start of the 2018-19 campaign.