Aouar has been linked with Premier League outfit Arsenal, as well as Manchester City, Paris Saint-Germain and Chelsea following Lyon's memorable run to the 2019-20 Champions League semi-final.
Lyon value Aouar at €60million (£55m) and are refusing to lower their demands as Mikel Arteta's Arsenal struggle to raise the necessary funds.
Asked if Aouar could remain at the Ligue 1 club, Aulas told Le Progres: "Financially, Arsenal are like everyone else [in a tricky spot amid the coronavirus pandemic].
"And Houssem could say to himself that the best thing would be to stay with us."
Lyon captain Memphis Depay has also been linked with Barcelona and Milan, while Moussa Dembele continues to attract interest from across Europe.
"From the start I said that we would not lose the three players announced every day in the newspapers," Aulas said.
"Ten days before the end of the transfer window, none of the three have gone. And I don't imagine that will happen. If one or two leave, they will be replaced."
Lyon have endured a difficult start to the 2020-21 season, winning just one of their opening four matches to sit 12th in the standings.
But amid doubts emerging over head coach Rudi Garcia's future, Aulas insisted: "Rudi is with us. He has been cited as one of the best 10 managers in Europe. News gets invented, it is sad.
"We are not going to respond to such nuisances. Rudi Garcia is and will be our manager, that is clear. And we are going to have a great team."
Ronaldo signed a two-and-a-half-year contract with Saudi Pro League leaders Al Nassr last week, having spent over a month as a free agent after leaving Manchester United.
At his unveiling in Riyadh on Tuesday, Ronaldo declared he had nothing left to prove in Europe and insisted the move did not represent the end of his distinguished career.
The five-time Ballon d'Or winner may well have appeared in the Champions League for the final time, but he claims to have a fresh set of aims in Saudi Arabia – including contributing to the development of women's football in the country.
"It's a new challenge and I'm so glad that Al Nassr has given me this opportunity to develop, not only in football, but also for the young generations, and for women as well," said Ronaldo.
"Many people probably don't know, but Al Nassr has a women's football team as well. Women's football is very competitive here.
"I know what I want, and I know, of course, what I don't want as well. It's a good chance to change, to help with my knowledge and my experience to grow many, many important things.
"I want to give a different vision of the country from the footballing perspective of everybody. This is why I took this opportunity."
While Ronaldo – who could make his Al Nassr debut against Al Ta'ee on Thursday – will undoubtedly be the most high-profile star to have featured in the Saudi Pro League, club president Musalli Al-Muammar insists he will be treated differently to other players.
"During the negotiations, Cristiano made it clear that he wants to be treated like the rest of our players," he said. "He doesn't want special treatment.
"Ronaldo is the greatest player ever. We hope players learn from him and replicate his attitude."
Head coach Rudi Garcia, meanwhile, is not expecting any issues as he integrates Ronaldo into his squad.
"Ronaldo is one of the best ever. It's an honour for me and for Al Nassr to have him here," Garcia said.
"It's fantastic for the league and for the country to have Ronaldo here.
"He will be the easiest player to train. There's nothing to teach him. My goal is to make Ronaldo happy."
Roma head coach Jose Mourinho had been linked with a possible Ronaldo reunion, having coached the Portuguese at Real Madrid.
Spanish newspaper AS this week claimed Mourinho had been offered a two-year contract worth €100million.
For now at least, Al Nassr have put Jelicic in charge, promoting him from his position in charge of their under-19 team.
The Riyadh-based club said: "Al Nassr can announce that head coach Rudi Garcia has left the club by mutual agreement.
"The board and everyone at Al Nassr would like to thank Rudi and his staff for their dedicated work during the past 8 months.
"We can announce that our U19 coach, Mr Dinko Jelicic will be the new head coach for the first team. Good luck, Mr Dinko."
Frenchman Garcia was a Ligue 1 winner as head coach of Lille in 2010-11 and the 59-year-old has also bossed Roma, Marseille and Lyon.
He was appointed in late June last year and departs with Al Nassr sitting second in the Pro League with seven games remaining, three points behind leaders Al Ittihad, to whom they lost last month.
Ronaldo's arrival as a free agent after his release by Manchester United was announced in late December, and the 38-year-old superstar has drawn unprecedented attention to the league.
Real Madrid's record scorer spent three seasons playing under fellow Portuguese Mourinho at the Santiago Bernabeu from 2010 to 2013, and it remains to be seen whether they are reacquainted in the future.
Jelicic gets the chance to lead the team for now, and he may make the job his own.
Should Al Nassr fall short of overhauling Al Ittihad, however, they may have reason to think again, and it could prove less disruptive to prise away a top coach of Mourinho's ilk during the close season rather than at the business end.
