Arsenal have had a £29m bid snubbed by the French club, who yesterday issued a statement denying claims they have received a second offer from the Gunners.
French publication L'Equipe claim Arsenal will return with a £33.5m in the coming days.
But it is unlikely to succeed because Get French Football News report that Lyon view the potential sale of Lacazette as "suicide".
**ARSENAL TRANSFER NEWS: WHO DOES WENGER WANT? WHO HAS SIGNED? WHO COULD LEAVE?**
Arsene Wenger has publicly slammed Lyon for going public about his bid for the striker.
"Lyon are comfortable with their own statements," Wenger said.
"I think in situations like this it is always best to keep things as secret as possible.
"If we sign someone, we will announce it. Until then, I can't say much more than that."
Lacazette made 34 Ligue 1 appearances last term, scoring an impressive 21 goals.
He has three years to run on his current deal after putting pen to paper on an extension last summer.
Wenger has already been snubbed by Jamie Vardy in his hunt for a new striker this summer.
Gonzalo Higuain was linked with a move to Arsenal but Juventus beat them to the punch.
