Kenyon is in the southern French city to secure the signing of Essien, Jose Mourinho's last summer transfer target, but not, despite Roman Abramovich's unparalleled purchasing power, at any price. Chelsea are now trying to work to a budget, albeit one which is still larger than anyone else's.
Aulas, under pressure for constantly selling his club's leading players, and for subsequently failing in Europe, wants £32m for the Ghanaian. Chelsea, unsurprisingly, regard that as a high price for a 22-year-old player without experience either in the World Cup or Europe's big four leagues, even if he was voted French player of the year last season by his peers.
Chelsea had hoped to secure Essien's signature before their American tour but had to head to New Jersey last week without him. That failure has forced Kenyon to come back across the Atlantic and mount another attempt to complete the deal.
Chelsea's ultimate deadline is the end of the transfer window. "As long as Essien is here by 31 August we will be happy," Kenyon said. However, Mourinho would like his jigsaw pieces in place earlier, preferably before the Community Shield on 7 August while the Lyon coach, Gérard Houllier, needs to finalise plans for his first season in charge of the French champions. With Manchester United, Barcelona, Real Madrid and Juventus, Essien's other suitors, no longer pursuing a deal Aulas's position has been weakened.
At least Essien wants to join Chelsea, as he made clear when he said "My last hope is Abramovich. I hope he will meet their demands."
This will have been more of a relief than one might expect to the English champions. Abramovich may have the deepest pockets in the game but Chelsea have failed to secure a series of high-profile targets this summer, notably Steven Gerrard, Andrei Shevchencko and David Trezeguet.
The latter revealed yesterday that he was never remotely tempted by the prospect of leaving Juventus for Stamford Bridge. The 27-year-old French striker said: "I was in the United States on holiday and did not really follow Chelsea's interest in me. I feel very happy with Juventus and I never thought I could leave."
Instead, Trezeguet finds himself playing alongside his France team-mate Patrick Vieira, who has joined Juventus from Arsenal. "I am delighted. We all know his qualities. He has been Arsenal's symbol in the past few years. He will surely bring us something extra and I agree with coach Fabio Capello when he says that, with Emerson, he makes the best pair of central midfielders in the world."
Even without buying Trezeguet, Chelsea have already spent £32m this summer taking the total expenditure on transfers under Abramovich to £242m in barely two years. Only Real Madrid and Milan have come close to matching their spending this summer, each laying out more than £20m, primarily on Robinho and Alberto Gilardino respectively.
Both clubs' largesse will be matched by Arsenal if they can persuade Juan Baptista to leave Seville. Unlike Chelsea, however, Arsenal, had to sell a key player before trying to cut such a swathe in the market.