The pair played up front together for Chelsea until Anelka left for Shanghai Shenhua in January.
Having settled into his new surroundings, the 32-year-old is keen to be joined by Drogba and another of his former teammates while at Paris-Saint Germain, Selim Benachour.
"I hope Selim Benachour and Didier Drogba will quickly join us," Anelka told Le Journal du Dimanche. "I hope they come. It is up to the club to see if we have the right means."
Anelka has recently taken on a coaching role with Shenhua to run alongside his playing duties.