Manuel Pellegrini is determined to keep hold of Marko Arnautovic amid interest from the Chinese Super League in the Austrian forward.
An unnamed club, believed to be champions Shanghai SiPG, is understood to have launched a £35million swoop for the Hammers' top scorer.
The club will attempt to lure Arnautovic, who turns 30 in April, with wages understood to be £200,000 a week over a four-year contract.
Hammers boss Pellegrini insisted no concrete bid has been made, but he did admit it could be difficult to hang on to his star man in the future.
"Those are all rumours," he said. "We know that we have a very good player in Marko, a lot of clubs may want him to play for them. At the moment we have no news about him.
"I don't want to talk about things that might happen. Marko in this moment is a player of our team, players of his quality and other players like Declan Rice, Felipe Anderson, other clubs will want them but that is one thing. I don't think they will go.
"I want to keep him, of course, but you never know what might happen in the future."
West Ham host Arsenal on Saturday and Pellegrini has no qualms about picking Arnautovic despite the speculation.
"Marko and all the other players involved in rumours have their heads here," he insisted.
"They want to continue playing the way they have been so far and I am sure that he will have his head in the game against Arsenal."
Gunners old boys Samir Nasri and Lucas Perez will be in the squad to face their former club.
Perez, who has struggled for game time with West Ham since leaving the Emirates in the summer, is another being heavily linked with a move away this month.
Nasri, by contrast, impressed on his Hammers debut against Birmingham in the FA Cup.
Pellegrini said: "Lucas is part of our squad and for the moment he will continue with us.
"It was very useful for Nasri to get minutes against Birmingham, he played 60 minutes, he has working with us very hard for around 40 days now so he has demonstrated he is able to play and he will be involved in the game against Arsenal."
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