Anelka joined the Chinese side on a two-year contract in January.
Drogba’s current contract with Chelsea is set to expire at the end of the season.
“I personally would like to see Drogba join Shanghai Shenhua,” Anelka said.
He added: “Yes I am frequently in contact with him. I think Drogba should be joining us, if all goes well, but that is not my position to announce.”
