The Ivory Coast striker, who will play at the January 21-February 12 Africa Cup of Nations, told France Football magazine he wanted to "find again more fun, shivers, fervour, pressure and passion on the field."
Asked if it meant he would leave Chelsea, Drogba, who joined the London club in 2004, said: "Not before June anyway."
His former Chelsea team-mate Nicolas Anelka joined Shanghai Shenhua, coached by former French international Jean Tigana, earlier this month.
Shanghai have also expressed an interest in Drogba and British media reported that the 33-year-old could be set for a lucrative summer move to China when his Chelsea contract expires at the end of June.
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