The 25-year-old Frenchman, who was a shock exclusion from Les Bleus’ EURO 2016 squad, has dominated headlines in recent weeks with talk surrounding his future plentiful.
Arsenal are believed to be big admirers of the goal-getter, with a move before the close of the transfer window expected.
However, the Gunners’ plans have taken a hit, with West Ham having reportedly had a £42.7m offer knocked back by Lyon, who are unwilling to sell.
The Hammers failed with a bid of around £31m earlier in the summer but seemingly revived their interest in the attacker.
However, Lyon are in no rush to let their key man go, while Lacazette himself is demanding Champions League football, something West Ham cannot offer.
The news will come as a blow for Arsenal, who now look likely to have to pay a huge fee to land the hit-man.