Arnautovic wants to quit West Ham for a big-money move to China with Shanghai SIPG believed to be offering to almost treble his wages.
Two seasons ago France midfielder Payet, another fans’ favourite at the London Stadium, refused to play until he got a move back to his former club Marseille.
Pellegrini says he does not blame Arnautovic for having his head turned but is convinced the Austrian forward will continue to do his best for the team, even if the move does not come off.
“Marko is working with the team without any problem,” said Pellegrini.
“When you have such a high offer, everyone wants to leave but he has a contract here and we will know what will happen about it in the coming days.
“Of course you can’t blame him, he knows what is the best option for him and now we will see what happens between the clubs.
“I don’t think that the player will refuse to play.”
Arnautovic appeared to wave goodbye to the fans when he was substituted during West Ham’s home win over Arsenal last weekend, but as things stand he will be in the squad which travels to Bournemouth on Saturday.
Javier Hernandez will also be involved after overcoming back and hamstring problems, and Pellegrini brushed off speculation linking the Mexico striker with a January move away from east London.
“These are all just rumours, about so many players that will come to West Ham or go from West Ham,” added Pellegrini.
“Javier is part of the squad. Unfortunately for him he has had two long injuries this season for about five weeks every time.
“He will continue to be an important player for us.”
Ryan Fredericks has also resumed training following an ankle injury but Jack Wilshere will again miss out against the club where he spent a season on loan due to his ankle problem.
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