The Ghana international has failed to establish himself as a first-team regular at Stamford Bridge since returning from a loan spell at Real Madrid, making just nine appearances this season in all competitions.
Agent Fabien Piveteau explained there was an interest from Milan in his client - who is keen to play regularly ahead of the FIFA World Cup - but said no offer had been made.
"Milan have to first speak with Chelsea and they have to decide what they want to do with Essien," Piveteau told Spazio Milan.
"We have not yet opened any direct talks with AC Milan but this does not mean he cannot move to Italy. Clearly this is a great opportunity for my player."
Milan, 11th in Serie A, are believed to be on the verge of appointing Clarence Seedorf as head coach following the departure of Massimiliano Allegri on Monday.
And Essien would not be put off a move to the San Siro despite a difficult season, Piveteau confirmed.
"Milan are still in the running in the Champions League and are a great club, despite the difficulties of the moment," he added.
"(Essien) is fine and wants to play ahead of the World Cup, where he intends to do well with Ghana.
"We are fascinated by the Milan hypothesis and, from here to the end of the month, we want to explore all the requirements."
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