The negotiations have foundered over the last week on Lyon's mistaken belief that Chelsea offered £32m for their first-choice player in that position - Steven Gerrard. The London club have refused to repeat that price in their pursuit of Essien.
However, the actual price offered to Liverpool last month is understood to be significantly lower than that and Chelsea have no intention of dramatically outbidding the few rivals they have for the 22-year-old.
Although Aulas has stood firm in the face of constant pressure from Essien for a move to Stamford Bridge - including a sending-off for the player on Friday during Lyon's pre-season tour of South Korea - Chelsea believe they can secure the player for around the same £21m as they paid for Shaun Wright-Phillips.
The difficulty has been convincing Aulas that the club were never prepared to pay £32m for Gerrard. Although Lyon have publicly said that they want the same for Essien they have told Chelsea that they will accept £25m - a price that Chelsea's chief executive, Peter Kenyon, considers unacceptable.
Yesterday Aulas said: "The negotiations have not stopped but I told him [Peter Kenyon] that I will not discuss after 21 July or 25 July.
"With Michael we have a lot more chances to win a fifth French title next year but if he leaves it cannot be at a price that is lower than that asked for the best players in the world. Chelsea had accepted Liverpool's price for Steven Gerrard so I told Chelsea that Michael would only leave at Gerrard's price.
"We are not necessarily obliged to sell to develop the club. I am ready to keep Essien for another year and transfer him next year for a much lower price."
Chelsea will embark on their tour of America today after beating Benfica 1-0 in Lisbon and maintaining Mourinho's unbeaten record in visits to the home of his former club.
There are no further negotiations over Essien's future expected until he returns from South Korea and it would be unlikely that he could sign in time to join up with the squad before they return to London on 1 August. Aulas said: "He is usually very happy, smiling and enthusiastic about everything. I don't think he does it on purpose to be that sad. He is truly unhappy."
Mourinho said that Wright-Phillips would provide Chelsea with the balance they have lacked and increase the "internal competition" among his group of international wingers
Wright-Phillips said: "I just want to try and get some medals and be a regular part of the team."