The 34-year-old has been heavily linked with a move to the Far East following his release from Chelsea after last month’s Champions League triumph over Bayern Munich.
Shanghai Daily has claimed the club have entered the ‘final round’ of negotiations with the Ivory Coast international.
A move to the Chinese Super League side would see him reunited with former Blues team-mate Nicolas Anelka.
And new manager Sergio Batista has boosted hopes that the powerful front-man will arrive at the club next month
"The possibility of Drogba coming is still relatively large," former Argentina head coach Batista said on Thursday.
"I believe the club's management is still in contact with Drogba," concluding that he expects no deal to be announced before the end of the month.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.