The saga took it's latest twist yesterday when the French side rejected Chelsea's offer of £21m for the midfielder.
But the final lap of this particular marathon will take place next week when Lyon president Jean-Michel Aulas meets Blues owner Roman Abramovich.
The club said: "Jean-Michel Aulas has accepted the principle of a rendezvous with Roman Abramovich at the start of the next week in the south of France.
"But Lyon are worried about Chelsea's repeated efforts to get the agreement of Michael Essien by all means."
Earlier on Thursday, Aulas accused Chelsea manager Jose Mourinho of "unceasingly" telephoning Essien.
And he told French newspaper Progres that he expected Chelsea to pay £31m, and offer a player in part-exchange.
"They shouldn't take French clubs for fools," said Aulas.
"Michael is worth between 45 and 50 million euros (£31-35million) and because time has been wasted if we are to recruit if Essien leaves us now, I estimate that our player will leave for 45 million euros, while bringing in one Chelsea player.
"Rather than unceasingly calling the player to make it all the more sad, Mourinho would do better to call me directly. Chelsea will learn to know me."