The former Chelsea stars are in the middle of a cash row involving the club's owners.
The London Evening Standard says Zhu Jun is threatening to withdraw his funding unless he is given more control of the club by the end of the month.
Without the billionaire's money, Shanghai would be unable to pay their two former Chelsea stars, with Drogba on £250,000 a week and Anelka on £200,000.
"Now, I made a difficult decision to believe you one more time, one last time! And this time I have a deadline: two weeks," Zhu wrote on Weibo.