Aulas was quoted in the French press on Friday afternoon as saying: "Alexandre Lacazette was told he could leave".
Aulas has now confirmed the deal is off and that no other offers have been submitted for the 26-year-old, who scored 37 goals in 45 games last season.
The French global striker has been regularly linked with a move away from the Ligue 1 side with the Gunners and Spanish giants Atletico Madrid rumoured to be the most interested parties.
Lyon president Jean-Michel Aulas has stressed that no new offers have been made for striker Alexandre Lacazette since his move to Atletico Madrid broke down.
According to L'Equipe, Giroud has been told he is free to leave the club this summer and could move back to France. "For us, he is with Lyon", Aulas said at the presentation of new left-back Fernando Marcal, signed for €4.5million on Thursday.
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With reports from Italy and Egypt today both suggesting that Liverpool will give in to AS Roma's demands and up their bid for winger Mohamed Salah - a right sided player - it is recommended that you take these Lacazette rumours with a pinch of salt.
With uncertainty surrounding Lacazette's future, Chelsea forward Bertrand Traore, who spent last season on loan at Ajax, is being targeted.
'We want to bring in Bertrand Traore.
Roberto Firmino is brilliant but a poor finisher, while Daniel Sturridge's injury history means we can't rely on him in four competitions.
Lyon sold Corentin Tolisso to Bayern Munich for an initial €41.5m on Wednesday and Rachid Ghezzal is set to leave for AC Milan.