Shenhua, bankrolled by colourful video-game mogul Zhu Jun, signed Drogba's ex-Chelsea team-mate Nicolas Anelka in December and they have been in talks with the Ivory Coast international since at least January.
"As of now, Shenhua's negotiations with Drogba are continuing just as planned," Zhu told the Oriental Sports Daily.
Drogba, 34, revealed he was quitting English Premiership giants Chelsea on Tuesday, just days after his match-winning performance in the Champions League final against Bayern Munich.
Drogba scored a late equaliser as well as the decisive spot-kick in the penalty shoot-out. Since joining Chelsea from Marseille in 2004, he has tallied 157 goals in 341 appearances, helping the club win 10 trophies.
"It has been a very difficult decision for me to make and I am very proud of what we have achieved, but the time is right for a new challenge for me," he told Chelsea's website.
Drogba would be the latest star signing for China's increasingly big-spending Super League, after World Cup-winning coach Marcello Lippi joined Guangzhou Evergrande last week.
But Anelka's move has not been without its problems. Last week he threatened to quit Shenhua over the club's plans to hire a new head coach, according to local media.
"If there is still no one to support me and (they) continue to play little tricks behind my back... then I will quickly decide whether or not to retire," the Frenchman told the Xinmin Evening News.
Club owner Zhu has written to Anelka's agent and lawyer asking for an explanation, the Oriental Sports Daily said.
In April, Shenhua sacked French coach Jean Tigana, then the highest profile manager to work in China, after just a handful of games and replaced him with a makeshift set-up including Anelka as player-coach.
They are now tipped to be targeting Sergio Daniel Batista, who led Argentina to Olympic gold in 2008, as their new manager.
Drogba is one of the Premier League's most successful strikers and he departs Chelsea as their fourth all-time highest scorer. His 34 goals in European competition is a club record by 10 goals.
During his eight seasons at Stamford Bridge he won three Premier League titles, four FA Cups, two League Cups, and the Champions League title.