Anelka has railed against Shenhua management in recent days.
"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 said.
"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."