West Ham failed with a bid of more than £40m for Lyon striker Alexandre Lacazette this summer, the French club's president has said.
A bid of 50 million euros (£42.7m) was tabled by the Hammers, according to Jean-Michel Aulas.
However, Lyon refused the offer, Aulas told French broadcaster SFR Sport, just as he announced in July that Arsenal had seen a bid for the France international rejected.
Aulas said in a studio interview: "We've refused an offer of 50 million euros from West Ham for Alexandre Lacazette. We've even turned down more for him."
Lacazette, 25, has been a consistent goalscorer in France's Ligue 1 for the past three years, earning 10 caps for Les Bleus in that time.
West Ham boss Slaven Bilic lost Andy Carroll to injury early this season and new signing Andre Ayew joined him on the sidelines after suffering a thigh problem.
The club, who moved into the London Stadium for the new campaign, brought in another forward on Sunday when confirming the arrival of Italy international Simone Zaza on a season-long loan from Juventus.