West Ham have been heavily linked with the French international.
West Ham have been heavily linked with plenty of new strikers this summer, as it is a position that The Hammers need to find improvement.
The Lyon goal-machine has been linked with plenty of Premier League teams recently and reports have suggested West Ham might have already made a bid for the player.
Now the outspoken Lyon president Jean-Michel Aulas has admitted that West Ham did indeed make a bid for the player – but it was rejected by the club.
He is quoted by Sky Sports as telling Le Progres:
"For a sale to be made, all three parties must agree. We have refused several offers, the most important from West Ham for €40 million (£31 million) and we refused it."
Aulas also admitted that Lacazette was not necessarily not for sale. He is worried about leaving a sale too late and ending up in a similar situation to rivals Monaco last season, after they sold Anthony Martial to Manchester United:
"I do not want on August 28, ahead of the Champions League, to find ourselves in the same situation as Monaco [who sold Anthony Martial to Manchester United last summer].
"Ideally, he will stay. If he has an offer that he can't refuse then it will come through me, and that's it."
Lacazette has been linked with a number of clubs in recent weeks, owing to his excellent form in the French top flight in recent seasons.
The French international is hot property and Paris Saint-Germain and Tottenham Hotspur have also been linked with the player.
West Ham are believed to be looking for a new striker as Andy Carroll has battled injury problems throughout his West Ham career – as has Diafra Sakho and Enner Valencia.