The 33-year-old Ivorian international is entering the final six months of his contract at Stamford Bridge, and despite having talks over a new deal, no agreement has yet been reached.
Blues boss Andre Villas-Boas is keen to keep Drogba in west London, but is only willing to offer the African ace a one-year extension.
Drogba is holding out for a two-year contract, and will now reportedly consider following former Chelsea teammate Nicolas Anelka to the Far East.
Anelka completed a move to Shanghai Shenhua - one of three sides interested in securing Drogba's services - though the most appealing offer is likely to come from Guangzhou Evergrande, who are ready to offer him up to £400,000-a-week in wages.
Drogba has been with Chelsea since 2004, and netted his 150th goal for the club in the 3-1 home defeat by Aston Villa on New Year's Eve.
Having spoken of his desire to remain in west London it is by no means certain he will leave England, providing he is offered a contract which he feels he deserves.