Last month Shenhua announced the signing of French striker Anelka, in the most high-profile deal yet for the scandal-plagued Chinese league.
"We have been talking with Drogba," a Shenhua spokesman told AFP.
"But the situation is more complex than that of Anelka. We cannot say we are sure to sign Drogba, he said.
Chinese media have said the club could sign Drogba, who is from the Ivory Coast, as early as this week.
"Everything is going well so far, though there have been a few obstacles," the Shanghai Daily newspaper Thursday quoted Shenhua board member Zhou Jun as saying.
In December Chelsea manager Andre Villas-Boas said Drogba's Chelsea future remained unresolved.
Shenhua will sign another foreign player, Australian striker Joel Griffiths on Thursday, the spokesman said. Griffiths has previously played for Chinese club Beijing Guoan.
Shenhua has been on a spending spree of late, also bringing on board French coach Jean Tigana, former Fulham and Monaco boss.
Chinese football has long been mired in scandal, but clubs enriched by the country's industrial boom are suddenly spending big on players, starting with $10 million Argentine midfielder Dario Conca last July.