Grenier has been strongly linked with a move to the Premier League, with Arsenal and Liverpool both reported to be interested in the midfielder.
Juventus are also rumoured to be keeping tabs on Grenier, who recently stated that he has 'more or less' made a decision on which club he will join.
However, Aulas does not want to see Grenier move on this summer, telling reporters: "We've had talks about Clement Grenier.
"The club's position is there will be no departure this year of a player who was educated at the club and that is reaching maturity."
The future of Gomis is also uncertain as the Lyon striker is out of contract next summer, and has previously been linked with Cardiff City, Chelsea and Liverpool.
Aulas added: "We don't want a player who is quoted at €15million (£12.7m) to leave as a free agent."
Another player long linked with a move away from Lyon is Yoann Gourcuff and Aulas is waiting to see if there will be any interest in the playmaker.
"I don't know if there will be offers," he continued. "But his current level should attract some clubs."