West Ham rejected a £35million offer for Arnautovic from unnamed Chinese team.
And in a statement, the Austrian striker’s brother Danijel stated the striker wanted to leave the London Stadium.
But the club has hit back in an 18-word statement saying: “Marko Arnautovic has a contract and we fully expect him to honour it.
“He is not for sale.”
Just an hour before West Ham’s response, Arnautovic’s brother, who also works as his agent, insisted the 29-year-old wanted to challenge for titles.
“West Ham bought Marko for peanuts. They paid £20m for him, which is nothing in the current market,” read Danijel’s statement, which he gave to talkSPORT.
“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.
“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.
“Marko is professional and is preparing himself for the Arsenal game. He will give 100 per cent for West Ham. That is Marko. He will never change.
“Until he is no longer a West Ham player, he will give everything to the club. He hopes the fans can respect his wishes.”
As well as interest from China, Chelsea are also said to be considering a move for Arnautovic.
But Hammers boss Manuel Pellegrini has also expressed his determination to keep hold of him.
Pellegrini said: “We know that we have in Marko a very good player so maybe a lot of clubs may want him to play for their team, but he’s a player of West Ham and at the moment we don’t have any news about him.
“Marko and the other players involved in the rumours have their heads here, they want to continue the way they’re playing.
“I’m sure things like that are parallel to performance and he’ll have his head in the game against Arsenal (Saturday 12.30pm).”