The Ligue 1 club confirmed they had rejected a bid of €35m for Lacazette from Arsenal, and that they want to offer him a new deal.
According to L’Equipe on Saturday, Lyon have offered Lacazette a five-year contract worth around €6.5m/season.
Lyon’s president, Jean-Michel Aulas, has been in touch with David Venditelli, Lacazette’s representative, over a new contract, but still needs to discuss a potential release clause.
L’Equipe say Ligue 1 doesn’t allow insertion of release clause, but still both parties could agree to one through a private agreement.
It’s been reported the release clause could be as high as €70m, as both parties continue to negotiate over a new contract.
The 25-year-old has already scored 6 goals in three league games this season, and has another three years left on his current deal at Lyon.