Arnautovic's brother, Danijel, has issued a statement claiming that West Ham bought him for "peanuts" and should let him leave.
Arnautovic joined the Hammers from Stoke in a £20 million deal in the summer of 2017 and won the club's player of the year award after scoring 11 goals in his debut season.
Now joint top of the club goalscoring charts with eight, Arnautovic is under contract until 2022.
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 was believed that West Ham were ready to offer the Catalans giants £20 million for the services of the Spain global, but a source inside the London Stadium poured scorn on that notion.
We know Marko is a very good player so maybe a lot of clubs will want him to play for their team but at the moment he is a West Ham player and we want to keep him. It is close to double what they paid for him.
Wilson may be the answer to the forward search and he's proving this season he can tear it up in the Premier League.
"It is his great desire that West Ham accept the offer from China", Danijel added.
It is understood West Ham will not consider selling him this month because of the difficulties they may face in replacing him.
West Ham have had some miserable failures in attack for the club over the last decade, with the likes of Mido, Benni McCarthy, Marouane Chamakh and Simone Zaza all struggling upon arrival. At the moment we have no news about him.
'I think Marko and all the other players involved in rumours have their heads here and want to continue playing the way they are doing so far.
"Those are all rumours", said Pellegrini.
At times temperamental, Arnautovic was unhappy at being substituted during Saturday's 2-0 FA Cup win over Birmingham but Pellegrini played down the altercation, saying: 'He [Arnautovic] was angry for just one minute, that is it.' Asked last week about potential interest during the January transfer window, Pellegrini said: 'I am sure Marko Arnautovic will stay here with us'.
Will be hard to replace but i trust Pellegrini to do it. [tomster36]This whole thing about Arnautovic is annoying! Although after Payet you never know what's round the corner.