He has moved to rule various possibilities in and out amid intense speculation regarding his next move, with there a chance that he could take on a new challenge in France.
Mourinho has told beIN SPORTS: “I can imagine myself as a coach in Ligue 1.
“I am a man who has worked in four different countries. I like to know other cultures. Working in a new championship would be a fantastic experience.”
In the wake of those comments, it was immediately suggested that Lyon could be among those tempted to make a move.
The opportunity to work with an exciting young squad would likely appeal to Mourinho, but Aulas claims an agreement on the terms a proven winner is accustomed to would be impossible.
He said in L’Equipe when quizzed on contact with Mourinho: “I saw him last summer in Moscow, we talked a bit, but not about him coming to Lyon, on transfers.
“The Special One is not compatible with our economic reality.”
Mourinho is not the only high-profile coach to have been linked with Lyon, with Laurent Blanc another of those reported to be in the frame.
Aulas, though, has told RMC of the speculation: “You are constantly hearing of managers who want to come to Lyon. I am delighted.
“I heard a great French manager, who was the manager of PSG. I heard a great Portuguese manager who was the manager of Manchester United.
“I heard a lot of managers hypothesise about coming to Lyon. We are not going to have discussions with other managers in the coming days.”
While no imminent talks may be planned, Lyon may be about to find themselves in the market for a new manager.
That is because current coach Bruno Genesio has been informed that his contract will not be automatically extended after failing to guide the club to the Coupe de France final and a top-three finish.
On the back of a 3-2 semi-final defeat to Rennes in knockout competition, Aulas said: “I met with Bruno. We had agreed that if we went to the final and finished on the podium, there would be a two-year extension.
“I was happy to propose this renewal because I think he's done a very good job.
“Unfortunately, we will not go to the final... the decision will be made at the end of the season. I thank Bruno... he's had good performances, he is discreet and he respected the deal.
“I am sad that I cannot announce the extension. I had planned to make this announcement at the end of the season, but Bruno wanted to know.
“The extension is not totally ruled out but it will depend on the results. He may also want to listen to the other offers.”