Arsenal have had a €35m (£29.4m) offer for Alexandre Lacazette rejected by Lyon who warned the Gunners and other interested parties that the striker is not for sale.
In a club statement Lyon dismissed reports in the French press that Arsenal had offered up to €48m for Lacazette.
The speedy striker, who has scored over 20 goals in the last three seasons, has also been monitored as a potential signing by Tottenham and West Ham this summer.
But Lyon say Arsenal's bid had not been considered "for the sole reason that OL will keep Alexandre Lacazette who is considered irreplaceable and one of the key leaders of Bruno Genesio's squad".
It marks the second time Arsenal have been rebuffed in an attempt to land a new striker this transfer window after Jamie Vardy turned down a £25m move to the Emirates in favour of staying at Leicester.
The 21-year-old Japanese striker Takuma Asano and 20-year-old centre-back Rob Holding, who joined from Bolton last week, are the only additions Arsene Wenger has made since signing Granit Xhaka for £30m in May.