The 33-year-old Ivory Coast striker has scored nearly 150 goals for Chelsea since moving from Olympique Marseille in 2004 for 24 million pounds and has helped the club to win three Premier League titles and three FA Cups.
However, it now looks as if he will leave Stamford Bridge for nothing when his contract expires next year.
Drogba was weighing up lucrative options including possible moves to America, Russia or Asia, one of his agents, Thierno Seydi, was widely quoted as saying by British media.
"Didier has had the offer of a one-year extension from Chelsea. That does not suit us," Seydi said.
"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 yet."
Drogba might not be the only veteran forward on his way out of Stamford Bridge as Nicolas Anelka, 32, who has made only six appearances this season, has been linked with a move to Chinese club Shanghai Shenhua.
The former France international joined Chelsea from Bolton for 15 million pounds in 2008 and has scored more than 70 goals for the club.
