The 26-year-old striker has been watched by Arsene Wenger and his staff since breaking into the Lyon first team, where he scored 100 goals in 203 league appearances.
And while the Gunners' first bid for the player was rejected, negotiations have progressed in the second half of this week and a deal is understood to be close.
"At this moment, we have not reached an agreement with Arsenal for Alexandre Lacazette," revealed Jean-Michel Aulas, the Lyon president, as he unveiled new signing Mariano Diaz.
Mariano arrives from Real Madrid for €8m with a two-year buyback clause in his contract. The Madrid academy product is expected to be the replacement for Lacazette once Arsenal meet the Ligue 1 club's asking price.
"He wants to leave," Aulas said earlier this week.
"We will discuss it in the coming weeks. If so, offers will be heard, provided they match the value of the player."
Atletico Madrid have a long-held interest in Lacazette and expected to sign him this summer but the upholding of their transfer ban by the Court of Arbitration for Sport has altered their plans and they are instead pursuing their former favourite Diego Costa.
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