A Chinese Super League club, believed to be champions Shanghai SiPG, are understood to have launched a £35million swoop for Arnautovic, the Hammers' top scorer.
"It is his great desire that West Ham accept the offer from China", Danijel added.
However, the Premier League side are in no mood to lose the 29-year-old, who is the club's joint top-scorer with eight goals this season.
Samir Nasri admits that he was in tears thinking his career was over when he was handed an 18-month ban, but is glad he has been given another chance to do "the best job in the world" as West Ham gear up to face his former side Arsenal. "They paid £20m for him, which is nothing in the current market", read a statement from Danijel to talkSPORT.
They bought him to keep them in the Premier League last season and he did that.
'Now West Ham have a fantastic offer. Saturday is a new challenge. This is what he wants.
West Ham United fans are slowly coming to terms with the fact that Marko Arnautovic could be on his way out of the London Stadium after a £35m bid was made from the Austrian striker from an unnamed club in China. That is Marko. He will never change. He hopes the fans can respect his wishes.
"Marko Arnautovic has a contract and we fully expect him to honour it". He is not for sale'.
West Ham host Arsenal on Saturday and Pellegrini has no qualms about playing Arnautovic despite the speculation.
"Those are all rumours", Pellegrini said. "We are very [convinced] to play and to give big work in finding our victory".
"It took him a while to realise how good he was and he grew up a little bit as well". Marko in this moment is a player of our team.
"Jack Wilshere, I know him from when he first came in at Arsenal".
'I am sure his head will be in the game against Arsenal.
They have earmarked Bournemouth's England worldwide striker Callum Wilson as a potential target.
Since the move, he has had surgery on one ankle but then endured another enforced lay-off because of pain in the other ankle.