Lyon president Jean-Michel Aulas insists Alexandre Lacazette will eventually decide his own future, with West Ham still interested.
Reports earlier this week claimed the Hammers had seen a Â£31million bid rejected, and Aulas has now confirmed the rumours.
West Ham appear to be trying to begin their transfer business early, with bids for Bournemouth duo Matt Ritchie and Callum Wilson also turned down.
Lacazette has been linked with a move away from Lyon in recent months, with several European clubs impressed by his form in front of goal.
The 24-year-old has scored 48 goals in the last two Ligue 1 campaigns and Aulas admits he could still leave the club if an acceptable bid is made.
“For a sale to be made, all three parties must agree. We have refused several offers, the most important from West Ham for 40m euros and we refused it,” he told Le Progres.
“It is an answer that says I want to keep him, but I’m not sure because ultimately it is he who will decide.
“Ideally, he will stay. If he has an offer that he can’t refuse then it will come through me, and that’s it.”