The Austria worldwide has scored eight goals in 17 matches this season having moved from Stoke City to the Hammers in 2017 for around £20 million.
"West Ham bought Marko for peanuts", the statement read. It appears that he finds the offer from an unnamed Chinese club as the most appealing, according to a statement from his agent.
They are close favourites with the same bet firm at odds of (2.05).
The north London side are now fifth in the Premier League table after having beaten Blackpool 3-0 in the FA Cup third round last weekend. He wants to go to a new market and challenge for titles.
West Ham, 10th in the Premier League, host fifth-placed Arsenal on Saturday (12:30 GMT) and Pellegrini expects Arnautovic to play.
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The West Ham striker has recently returned to fitness and has been linked with a shock move to the Chinese Super League. "We know we have a very good player in Marko, a lot of clubs may want him to play for them".
The Austria forward moved to east London in July 2017 for £20m, plus an additional £5m in potential add-ons, and is West Ham's joint-top scorer this season with eight goals in all competitions. "It is his great desire that West Ham accept the offer from China", added Danijel Arnautovic.
"I predict with complete confidence that we'll look back at the whole thing and laugh on the day of Marko's testimonial in 2026 as he tearfully hangs his boots up and joins the coaching staff".
"Those are all rumours", Pellegrini said.
"They want to continue playing the way they have been so far and I am sure that he will have his head in the game against Arsenal". Callum Wilson is believed to be their primary target, but it would likely take a huge offer to prise him away from Bournemouth. But in some moments every club can sell some players, bring in another one and it's part of the process that you are doing to grow, so we cannot just talk about one name.
"If it was £50m between Wilson or Arnautovic I would go with Marko", he told The Debate on Sky Sports.