Drogba has turned down a one-year extension to his current deal at Stamford Bridge, which expires at the end of the season, when he would become a free agent.
The 33-year-old wanted two more years with Chelsea, but the club have refused to offer that length of contract.
Wealthy Chinese club Shanghai claimed in January they were in talks to sign the Ivory Coast international.
Shanghai paraded their new recruit Anelka to the Chinese media on Thursday, when his comments about Drogba reportedly caused a stir.
In press conference remarks, reported by the website of Shanghai-based Xinmin newspaper, Anelka said: "Yes, I often contact him. If all goes well, he should be able to come to Shanghai."
Anelka immediately clarified the deal was not done, adding: "Of course, if he can, which does not depend on me, but is to be determined by the club owners and investors."