West Ham maintain they do not want to lose their joint top-scorer, having already turned down a bid reported by British media to be 35 million pounds from a Chinese club.
"(On Friday) we will see the squad and which players are involved in the squad list," Pellegrini told reporters before West Ham head to Wimbledon in the FA Cup fourth round on Saturday.
"He is working with us without any problem."
While Pellegrini has said he is open to selling Arnautovic for the right price, he wants a quick resolution to the saga.
"Is it a distraction? As a manager, I am worried about many different issues in my squad," the Chilean coach added.
"Things happen in football and we know we must try to resolve this as soon as we can. I speak with all the players every day so I know what they want."
Pellegrini was handed some good news from the West Ham treatment room, with Manuel Lanzini returning ahead of schedule from a serious knee injury.
The 25-year-old midfielder, who had ruptured a ligament in his right knee while training with Argentina in June, joined up with his West Ham team mates for light training this week.
"He is just working part of the warm-up with the squad but the important thing is that he feels good and his knee is the correct way," Pellegrini added.
Another player returning from the sidelines is right back Ryan Fredericks, who returned to action for the Under-23 side on Tuesday after recovering from a shin injury.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
