Manuel Pellegrini admitted West Ham would consider selling Marko Arnautovic if the price is right.
The forward has been linked with a move to the Chinese Super League and his brother and agent recently said Arnautovic was keen for a transfer to go through.
Last week, West Ham issued a statement prior to their Premier League game against Arsenal insisting the Austrian was not for sale.
However, Arnautovic appeared to wave goodbye to supporters at the London Stadium when he was substituted during the win over the Gunners, and Pellegrini has now suggested that stance may soften were an acceptable bid to come in.
"When you have such a high offer, everyone wants to leave but he has a contract here," the Hammers boss told reporters.
"We will know what will happen about it in the coming days.
"If I say the player must stay, the player will stay. But I think as a manager the best thing is to take the solution that is best for the player and the club, both together.
"If it's a good deal for both parties we will arrange to be without Marko."