The 33-year-old striker has been linked with a move away from Stamford Bridge this month, with Turkish giants Fenerbahce also eager to sign him.
But the Ivorian told France Football magazine the announcement of his departure would be "not before next June."
According reports in China on Thursday, Shenhua were optimistic a deal for Drogba was not too far away.
"Everything is going well so far though there have been a few obstacles. They never turned us down, which is good for us," club board member Zhou Jun told The Shanghai Daily.
With Nicolas Anelka having recently signed with the Chinese side, Zhou believes the odds of signing the 33-year-old has shortened dramatically.
"It's like making a blockbuster film. When superstars like Jackie Chan, Jet Li and Zhou Xun have confirmed their participation, other actors and actress will be confident of the movie."
Drogba is currently with the Ivory Coast for the African Nations Cup.
Earlier this week, former Chelsea boss Carlo Ancelotti claimed the Blues would have to sell Drogba for Fernando Torres to flourish, a view rejected by current manager Andre Villas-Boas.
