He is due to meet Chelsea owner Roman Abramovich in the coming days as the Premiership champions look to add Essien to their squad ahead of the new season.
They have bid £21 million so far but Lyon want £30 million.
"It is tedious to lose one of the best players in Europe but he has not left yet," said Aulas.
"We can still find a compromise so that he only leaves next year.
"Chelsea will have to show themselves to be very persuasive for us to let him leave.
"Manchester want him just as much."