Lyon president Jean-Michel Aulas has confirmed that striker Alexandre Lacazette will not join Arsenal.
The Gunners made an offer to secure the services of the 25-year-old but the offer was rejected.
And Aulas has now revealed that the North Londoners will not make an improved offer for the player.
"Arsenal have not come back and will not come back," Aulas said.
"No-one will leave Lyon."
In a club statement released at the start of the week, the French side made it clear that the striker is not for sale.
"Arsenal made an offer of €35m which Lyon didn't accept for one reason alone – we will keep Alexandre Lacazette," read a statement released by the club.
"Lacazette is one of the main leaders of Bruno Genesio's squad.
"We categorically deny having received an offer of €48m [£40.2m] from Arsenal for him, as has been reported."