The 32-year old Frenchman is almost certain to depart Stamford Bridge in January and he could be on his way to China with Shanghai's media officer saying a deal could be agreed very soon.
"There'll be news very soon," Ma Yue told The Associated Press.
"There'll be news in four to five days, at the latest. In five days, we'll definitely have news on whether it is 'Yes' or 'No.'"
Ma understands that there may be some cynics out there regarding Shanghai's possible capture of Anelka but he says the impending arrival of former Fulham manager Jean Tigana as the club's new boss may further lure the ex-Arsenal and Manchester City ace.
"It's basically decided," he said of Tigana.
"He will be coming with his own team picked from France. Now you understand why Anelka might choose us."
It is believed that Shanghai could pay Anelka as much as £6million a year but Ma has indicated that those figures are not accurate.
"It's not convenient for us to give figures at the moment. The figures being spoken about outside are not necessarily correct," he concluded.