The statement said: "West Ham bought Marko for peanuts".
The former England Under 21 global may have been a peripheral figure for Newcastle but Manuel Pellegrini, West Ham's manager, admires Shelvey and would jump at the possibility to bring him to the London Stadium in this window.
Pellegrini dismissed Arnautovic's angry reaction to being substituted after 20 minutes of Saturday's FA Cup...
They posted on Twitter: "Marko Arnautovic has a contract and we fully expect him to honour it".More news: Phillies rumors: Expect Manny Machado decision in the next week
If Arnautovic does move to China, West Ham will make a move for Bournemouth forward Wilson.
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. "They paid £20m for him, which is nothing in the current market", read the statement.
With three weeks of the window remaining, though, there is a recognition that West Ham will continue to monitor Shelvey's situation and it could be they end up in a position where they can put pressure on Newcastle. We know that we have a very good player in Marko, a lot of clubs may want him to play for them.
The player's agent and brother Danijel Arnautovic told talkSPORT on Thursday it is his client's "great desire that West Ham accepts the offer from China".
Arnautovic has been a key performer under Manuel Pellegrini this season, scoring seven times in 15 Premier League appearances. He wants to go to a new market and challenge for titles.More news: AT&T gets burned by rivals over its fake 5G network
While West Ham would certainly have the funds available to sign a replacement during this window, recruiting prolific strikers can be very hard mid-season.
"I don't want to talk about things that might happen". I don't think they will go. At the moment it's all so slow and predictable and the whole game is being played in a 30-yard space.
"Those are all rumours", said Pellegrini.
"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: 5 women to watch at the Australian Open