This could mean the Ivorian player will not be heading to the UAE where Pro League side Al Wasl are bidding for him.
The Chinese Super League club have reportedly been in talks for months with Ivory Coast's Drogba, who would join Nicolas Anelka, his former Chelsea teammate, if the deal goes through.
"A top Shenhua official left for Ivory Coast for the final round of negotiations to sign star striker Didier Drogba," the report said.
The newspaper said a Shenhua board member, Zhou Jun, would hold direct talks with the 34-year-old player.
Speaking on Thursday, Sergio Batista, Shenhua's new manager, boosted hopes Drogba might join the club.
"The possibility of Drogba coming is still relatively large," Batista told a news conference, a transcript of which was posted on a Shanghai media website.
"I believe the club's management is still in contact with Drogba," he said, adding he did not expect news until after June 30.
Shenhua declined to comment on Friday.
Drogba left Chelsea after helping the English Premier League club to their first ever Champions League triumph last month.
Former Argentina manager Batista joined Shenhua, sitting ninth in the 16-club Chinese league, late last month after the club sacked French coach Jean Tigana and temporarily made Anelka player-coach.
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