West Ham said this month that Arnautovic was not for sale after his brother and agent Danijel said he wanted to sign for a Chinese club who have reportedly tabled a 35 million-pound bid.
West Ham manager Manuel Pellegrini said he will have the final say on the potential transfer but the Chilean had not asked the club owners to reject offers for Arnautovic.
"If I say the player must stay, the player will stay," Pellegrini told reporters.
"I don't have any problem with the club. They are not forcing me to sell Marko Arnautovic. In all the months I've been working here I never had any problems with the owners about that."
Former Stoke City striker Arnautovic is West Ham's joint top scorer this season with eight goals in all competitions.
Pellegrini, who spent two years managing Chinese club Hebei China Fortune, said he understood Arnautovic's desire to move to China due to the high wages on offer.
"If it's a good deal for both parties we will arrange to be without Marko," he added.
West Ham, who beat London rival Arsenal last weekend, sit ninth in the league standings.
(Reporting by Rohith Nair and Hardik Vyas in Bengaluru, editing by Ed Osmond)
