Drogba has confirmed he will be leaving the Blues when his contract expires after admitting the Champions League success was a fitting way to end his eight-year career at Stamford Bridge.
He has been heavily linked with a move to Shenhua and the Chinese club's owner Zhu Jun confirmed earlier this week that talks are going as planned.
However, when asked about the potential arrival of Drogba in the Far East, the Anelka preferred to pass on his congratulations to his old strike partner.
"About if I have anything to say to Drogba, I would like to say that I congratulate him on winning the European Champions League," Anelka told Shanghai Greatsport. "And this congratulation goes to everyone at Chelsea.
"He (Drogba) should be very proud that he leaves the club in this way.
"Chelsea has proven that it is one of the greatest clubs in the world and I am also proud that I used to be one of its players."