The 25-year-old has been offered a five-year contract worth €6.5m/season, reports L’Equipe on Saturday.
L’Equipe say Lyon could also insert a €70m release clause under a private agreement, as such clauses are not allowed in Ligue 1.
Lyon’s president Jean-Michel Aulas is in talks with with David Venditelli, Lacazette’s representative, over the final details of the contract, and both parties could agree to a deal soon.
Lacazette has started the season in an impressive way with six goals in three games.