The 33-year-old is in the final season of his £120,000-a-week contract and has turned down a new deal.
Drogba has also rejected a January move to Italian giants AC Milan and could be set for a move to Russia or Qatar next summer.
Drogba's agent Thierno Seydi, based in Senegal, claimed last night: "Didier has had the offer of a one-year extension from Chelsea. That does not suit us.
"We know what we want, where we want to go and what offers we have.
"AC Milan came in for Didier on loan with an option to buy but I said 'No' straight away. Their offer did not interest us.
"At Didier's age, he has nothing left to prove as a player. He will go where he is offered the most money.
"It could be the United States, Russia, Qatar or somewhere else in Asia.
"Once you are well into your thirties you have to go to a club where you can be certain you'll be able to pay your bills.
"LA Galaxy are a possibility among many others. He has been linked with Anzhi Makhachkala in Russia, as they pay well.
"But neither Didier nor I have had an offer from them."