The former Chelsea star missed a public training session on Tuesday, and Batista said he would make a final decision on Drogba’s inclusion in the squad nearer to the game.
“Right now we can’t say for sure because he has a back problem. We will see tomorrow,” said the Argentinian.
The Ivory Coast star made his debut in China last Sunday, coming on as a second half substitute to set up his side’s equalizer in a 1-1 draw away to Guangzhou R&F.
The highly-anticipated clash with United could see Drogba reunited with former Chelsea team-mate Nicolas Anelka for the first time since the pair left the English Premier League.
Drogba joined Shenhua in June on a two-and-a-half year contract reported to be worth around 200,000 pounds ($314,000) a week.
Batista suggested he may choose a second-string squad to play against Sir Alex Ferguson’s men, saying he would rest key players in preparation for Shenhua’s clash away to league leaders Guangzhou Evergrande on Saturday.
“Even though its just a commercial game we will still prepare for it seriously. But for us, the domestic championship is more important,” the former Argentinian national side coach said.
United players also appeared at the public training session and were watched by a cheering crowd of several hundred red-shirted Chinese fans.
Shenhua take on the Red Devils at the 80,000 capacity Shanghai Stadium.