The 34-year-old helped the Blues win the Champions League in Munich to bring the curtain down on a trophy-laden spell in west London.
Ivory Coast international Drogba - signed from Marseille for ?24million in 2004 - is now expected to join up with former Blues team-mate Nicolas Anelka at the Chinese Super League club on what would be a lucrative free transfer.
Shanghai Shenhua owner Zhu Jun is quoted as saying in the Oriental Sports Daily: "As of now, Shenhua's negotiations with Drogba are continuing just as planned."
Anelka, 33, joined Shenhua in January and is currently player/coach following the recent sacking of former Fulham boss Jean Tigana.
Source: PA
Source: PA