The 30-year old Argentine midfielder has been linked with the North Londoners in recent times although he was receiving interest from clubs in Spain and Italy.
OM boss Didier Deschamps confirmed that the Gunners are keen on some of his players – including Mathieu Valbuena and Andre Ayew – but insists the main target was Gonzalez who will remain at the Stade Velodrome this summer.
"The one that really interests them is Lucho Gonzalez," Deschamps said.
"Arsene Wenger believes that it is a great player who could be useful to his team even though he does not fit in with his recruitment policy.
"He wanted him on loan but it was not acceptable to us."