However the Hammers are now in a fight with the Chinese Super League for their second top scorer this season with a bid of £35 million tabled for the striker, from an unnamed team from the far east.
And it appears the bright lights and big bucks of China have caught the attention of the Austrian.
West Ham United star Samir Nasri has admitted that he cried when he thought that his career was over. "They paid £20m for him, which is nothing in the current market", read a statement from Danijel to talkSPORT.
Now he is back in the Premier League and he can not believe how things have turned around for him. "He took every award at the club; best player, signing of the season and the players" award.
A tough trip to the Emirates Stadium lies in wait for West Ham this weekend, a ground at which Nasri spent three years earlier in his career, and the two-time Premier League victor is determined to show his quality in what will be a "crazy" atmosphere. We know that we have a very good player in Marko, a lot of clubs may want him to play for them. Saturday is a new challenge. This is what he wants.
Arnautovic's brother, Danijel, has issued a statement claiming that West Ham bought him for "peanuts" and should let him leave.
In a plea for supporters to accept Arnautovic's decision, he added: 'He knows the West Ham fans love him and he has a special connection with them, but things move on, this is the world of sport and he hopes they can understand.More news: New York City launches $100 million universal health insurance program
More news: Taliban Calls Off Peace Talks In Qatar With U.S
More news: Shutdown cuts drivers off from Mount Rainier National Park
'I am sure his head will be in the game against Arsenal and it will not affect his performance'.
West Ham are now operating without creative playmakers Manuel Lanzini, Jack Wilshere and Andriy Yarmolenko due to injury, and although Samir Nasri has come in to help in their absence, the Chilean is looking for further signings, not just to add quality to his ranks, but also depth too. That is Marko. He will never change.
"Players of his quality and other players like Declan Rice, Felipe Anderson, other clubs will want them but that is one thing". He hopes the fans can respect his wishes.
But a Hammers spokesperson said: "Marko has a contract and we fully expect him to honour it". Arnautovic, who has scored eight goals this season and is the club's record signing, is a favourite with supporters.
Shanghai SIPG are the side said to be interested and have reportedly offered a wage packet of £200,000 per week over a four-year deal.
It remains to be seen whether Arsenal will bring in any new players this months during the January transfer window.