The Austria international pulled a hamstring in West Ham's 3-1 Premier League win over Cardiff City on Dec. 4 and missed their subsequent victories over Crystal Palace and Fulham.
Arnautovic was expected to be out until the New Year, but Pellegrini said the 29-year-old was ahead of schedule, although Saturday's match against Watford had come too soon for him.
"I think, next week, he will be back working with the team," Pellegrini told a news conference.
Arnautovic has been a key attacking player for West Ham this season, scoring five league goals in 13 games, but Pellegrini said his team had coped well without the forward.
"When you don't have those players, you have a squad. I am happy with the options I've had without Marko. I'm not happy about the injury but I'm happy with my squad," the Chilean added.
Pellegrini was less positive about Jack Wilshere's ankle problem, saying he was not sure how long the midfielder would be out or whether he required surgery.
Marko Arnautovic of West Ham United looks on during the Premier League match between West Ham United and Burnley
Image credit: Getty Images
"We don't know. We need to wait for the medical examination and we will know properly in the next days. But at this moment we cannot be sure what he needs."
Pellegrini said West Ham could bolster their squad by signing French midfielder Samir Nasri in January.
The former Arsenal and Manchester City midfielder has been training with the Hammers since last month as he approaches the end of his 18-month doping ban.
"We're going to take the decision next week. Samir is working with us well, he is losing weight, his mentality is to try and have a spot here with the squad."
West Ham are currently ninth in the league on 24 points, having won their last four matches.