Following the rejection of a bid of more than £20m, the Lyon chairman, Jean-Michel Aulas, has agreed to meet Chelsea owner Roman Abramovich to discuss Essien, the French club said in a statement yesterday.
"Jean-Michel Aulas agreed in principle to have a meeting with Roman Abramovich some time early next week in the south of France," the club said. "But Lyon want to express their concerns about the repeated attempts from Chelsea to gain by every means the agreement of Michael Essien."
The statement continued: "The club received a new offer from Chelsea. Even if the gap between Olympique Lyon's claim [they want £32m for the player] and Chelsea's offer has been narrowed, the two sides still have to set up a deal."
Essien did not play in Wednesday's 4-1 victory over Auxerre in the Trophy of Champions. It is still uncertain whether he will play in the opening Ligue 1 match of the season tomorrow at promoted Le Mans.
In the US, Chelsea were expecting a tough test on their pre-season tour with two matches against Milan, but it is the 16-year-old Adu who has given them most food for thought so far.
Adu is one of the biggest names in US soccer, having already made his mark at the Major League side DC United and it was his trickery which made Chelsea look sluggish, even though Jose Mourinho's side managed to pinch a 2-1 victory on Thursday night.
Chelsea have been linked with a move for Adu, who has already been compared to Pele, since he was 14 and it was no coincidence that Mourinho found time to have a chat with the teenage prodigy before start of the match .
If he wasn't aware of what excitement Adu brings to a side before the game, he certainly did after as the majority of the 31,473 crowd screamed at his team-mates to give the ball to the forward at every opportunity.
In one dazzling dribble, Chelsea's new signing Lassana Diarra was left not knowing which way to turn as Adu went through his array of tricks. The American fans cheered him like he had just scored, but they will not be so happy to hear that he is already eyeing a move to Stamford Bridge.
He said: "I definitely want to play for Chelsea one day. They're my favourite club in England. I spoke to Mourinho before the game, we were just having fun and he congratulated me on the goal I scored last week.
"He knew a lot about me already. Playing in the Premiership is a goal for me. I think I can achieve it if I keep working hard and keep my head on straight. When I am 18 I start exercising my options and I hope I get a call from a big club."
Joe Cole, who only played the first half for Chelsea, knows all about having to cope with the hype that comes with having great talent as a teenager. The England man watched Adu from the sidelines and was in no doubt that he could make the grade at Chelsea.
He added: "I thought Freddy did really well against us. He showed some nice touches. It's difficult to have a lot of pressure on young shoulders which I know all about but you just have to deal with it.
"He would be good at Chelsea. He's the sort of player who will be coveted all over the world because he's a talent and all the good players are linked with Chelsea."
Mourinho was not a happy man despite getting the chance to see Adu in action as DC United were quicker to the ball and took the lead when Bobby Boswell was allowed to climb unchallenged to head the ball past Petr Cech after 31 minutes. But their joy was short-lived as Shaun Wright-Phillips crossed for Damien Duff to volley home four minutes later and Hernan Crespo scored the winner, his first for Chelsea since returning from a season-long loan at Milan.
His striking rival Didier Drogba claims he is not feeling the pressure of losing his place despite Crespo's promising start. He said: "It's not a problem for me. It's good for my team-mates and for me to improve my game. We can play up front together and we are working like that in training.
"What more do I have to prove? We won the championship, I scored in the Carling Cup Final, I scored important goals, what do people want from me?"
Wayne Bridge also made his first appearance since he suffered a double fracture in his ankle at Newcastle over five months ago.