Unai Emery suggested Mesut Ozil did not deserve a place in Arsenal's squad as he sat out Saturday's Premier League defeat at West Ham.
The Gunners' highest-paid player has returned to full training over the last week following a knee problem, but was left out of Emery's travelling party completely as Declan Rice's first senior goal sealed a 1-0 victory for West Ham at the London Stadium.
Ozil has missed a number of games this season, with differing reasons given for his absence. A 2-1 win at Bournemouth in November was the only time Emery conceded the former Germany international was left out for tactical reasons.
The Arsenal head coach stuck with the side which beat Fulham in their last Premier League outing, but the visitors were poor as they failed to find the back of the net in a league game for the first time since the opening weekend of the campaign.
But when pushed over why he opted to leave Ozil at home for the short trip to east London, Emery claimed all of those players who did make the trip deserved to be there.
"I decided the idea of the players that I think are the best for this match," he said.
The 29-year-old's brother and agent claimed earlier in the week that Arnautovic wants to leave for the Chinese Super League and implored the club not to stand in his way.
Arnautovic was included in West Ham's side and was given a positive response by the home fans, although he waved to all corners of the stadium as he was substituted for Andy Carroll in the second half.
"We will see what happens in the next few days and I hope he will take the best decision," Pellegrini said when asked if the former Stoke man had been waving goodbye.
"I have been in this position a lot of time in my 30 years, but I'm calm with nothing 100 per cent sure (regarding Arnautovic's future)."
Although Ozil and Arnautovic were talking points, match-winner Rice was singled out for praise by Pellegrini.
The 19-year-old celebrates his birthday on Monday and has recently signed a new contract with West Ham.
He is yet to decide whether to represent England or the Republic of Ireland at international level, but Pellegrini is sure that whichever nation he opts to play for will benefit.
"I am sure Declan will be a top player," he added.
"He is improving in every game he plays, he is now more used to giving us a good build-up in front.
"I'm sure that we are seeing a top player soon and we will see not only for West Ham but also for the national squad that he decides to play for."