While the Ligue 1 club do not want to part with the sought-after attacker, the Frenchman is believed to want to leave
"There are exchanges and it's true that Arsenal are pressing," Aulas told RMC. "But the moment has not come. I am not ready to give an agreement in the current conditions to Arsenal."
The Gunners are €4m away from Lyon's valuation of Lacazette, 26, and negotiations look set to continue over the coming days as Arsenal hope to seal the deal for the France international.
Any move could end up costing the Gunners €55m (£48m/$63m) plus add-ons. There have been rumours of a swap deal involving Olivier Giroud but Aulas suggested it had not been discussed.
Instead, Diaz, who signed Friday after a reported €8m move, is expected to be Lacazette’s replacement.
The Gunners hope to keep Giroud, although they are prepared to let Lucas Perez - who joined last August but scored only once in 11 Premier League matches - leave the north London club this summer.
Arsenal remain hopeful of a deal for Thomas Lemar as well, but the youngster does not appear ready to force a deal to the Gunners.