Depay has been heavily linked with a move to Barcelona, while Aouar is reportedly a target for Arsenal.
But while the transfer window closes on 6 October (AEST), Aulas wants any departures from Lyon to be confirmed by Friday.
"I believe that we will tell the players that for everything that will not be settled in terms of departure before Friday, there will be no departure," he said.
"For us, the date of the transfer window will be Friday. I think to propose it tomorrow [Tuesday] to Rudi [Garcia, coach] and Juni [Juninho, sporting director].
"We realise that there is something wrong. It can be that and many other things. Friday, players who have not left will not leave."
Lyon has made a slow start to the Ligue 1 season, collecting just six points from its opening five games.