Anelka, 32, will move to the Far East in January on a two-year contract believed to be worth £8m a year, it was confirmed yesterday.
But, not content with just one former Stamford Bridge frontman, the Chinese Super League club have also approached Drogba.
Like Anelka, Drogba’s current contract expires in the summer, meaning he is free to discuss terms with other clubs next month.
Shanghai Shenhua director Zhou Jun said: “Drogba is an excellent player. We got in touch with him two weeks ago. From our club’s perspective, we have this to say: if he is willing to come, we will definitely welcome him.”
Drogba’s recent return to form has increased the 33-year-old’s hopes of being offered a new two-year contract in west London.
However, his advancing years raise questions about where he fits into manager Andre Villas-Boas’s plans to overhaul an aging squad.
Anelka is likely to be followed to Shangahi by former Fulham and Monaco coach Jean Tigana, whom Zhou confirmed had agreed a deal to take charge.