Lacazette, 23, is Ligue 1's top goalscorer this campaign with 21 strikes, helping Lyon into top spot ahead of Paris Saint-Germain, Marseille and Monaco.
His prolific goalscoring has led to apparent interest from abroad, but Aulas would like to see the Lyon youth product reach his peak at the Stade de Gerland – unlike the club's former striker Benzema.
"If we speak about efficiency, I think that Lacazette possesses the same characteristics as Benzema. The difference would be in their career," Aulas said.
"Alexandre could reach his highest level with Lyon. Karim had a specific path, a Merengue one. We gave him the chance to join the club he was dreaming to play with [Real Madrid].
"I would like to give Lacazette the chance to play for his dream club – the club he was trained with [Lyon]."
Lyon hold a one-point advantage atop the Ligue 1 table despite a 2-1 loss at Lille last time out.
While Lacazette has been a key part of their success, so has coach Hubert Fournier – who was appointed in May last year.
"Hubert Fournier is first of all a player. He played at the highest level. He played at his best level in Lyon," Aulas said.
"He knows the club and our spirit. He knows the chairman, the organisation. We knew we have a good relationship due to that synergy.
"Hubert has a lot of humility. He accepts and welcomes advice. We know that the best way to advise a head coach to reach the highest level, is to treat the club like a family.
"If they share the passion, we have to listen to everyone, whatever their position."
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