Per Ed Aarons and Jacob Steinberg of the Guardian, an unnamed Chinese Super League club have bid £35 million for the forward, although the Hammers have turned the offer down.
As noted in the report, in a subsequent statement, Arnautovic's brother Danijel made it clear the Austrian would like to move on:
"West Ham bought Marko for peanuts. They paid £20m for him, which is nothing in the current market. They bought him to keep them in the Premier League last season and he did that. He took every award at the club; best player, signing of the season and the players' award.
"Now West Ham have a fantastic offer. It is close to double what they paid for him. He wants to go to a new market and challenge for titles. This is what he wants. It is his great desire that West Ham accept the offer from China."
Following the statement, West Ham issued their own statement on their Twitter account, saying the player will not be going anywhere:
According to Aarons and Steinberg, a move to China would see Arnautovic earn a staggering £40 million over the course of a four-year deal. Shanghai SIPG are said to be the club interested in bringing the player to the Chinese Super League.
Steinberg said on Twitter the size of the deal is what Arnautovic finds attractive about the move:
Arnautovic is currently under contract until 2022 with West Ham and has been the team's star performer since arriving in the summer of 2017.
It's not the first time he's been linked with a move away. In November, Jason Burt of the Daily Telegraph said Manchester United were interested in the 29-year-old. Prior to those reports, Danijel had said the former Stoke City and Inter Milan man was "ready for the next step."
For West Ham the situation is far from ideal, especially when Arnautovic has been key to a recent run of fine form. Overall, since arriving at the club the Austrian has had a massive influence on the way the team attacks:
Throughout his career the forward has also had a reputation for being hard work off the pitch, as football journalist Seb Stafford-Bloor noted here:
Given the player wants to move and the fact he will turn 30 before the end of the campaign, there would be some sense behind selling for the kind of money mentioned, especially given West Ham would not be losing their talisman to a Premier League rival.
It does appear as if the Hammers are going to dig their heels in when it comes to their No. 7 though. You sense all eyes will be on the London club in the coming weeks to see how this transfer saga plays out.