It was reported in China that the former Chelsea striker was set to leave the club on Friday but after missing the match against Changchun Yatai, he has insisted he plans to stay
The Ivory Coast striker's future in Asia has looked in doubt for some time due to reports of unpaid wages at the Chinese Super League outfit.
In late August it was reported that chairman Zhu Jun had threatened to stop funding the team unless he was handed greater control due to his supposed unhappiness regarding the lack of money invested by other shareholders.
Drogba has previously denied that he has not been paid by Shanghai but the instability resurfaced over the weekend.
Chinese media reported on Friday that Drogba had told a journalist friend that he had been forced to leave the club due to the ongoing situation involving Jun.
Later that day manager Sergio Batista confirmed that the 34-year-old, along with other high-profile stars Nicolas Anelka and Giovanni Moreno, would not play in Saturday's match against Changchun Yatai, but claimed that all three players were injured.
In the evening, Jun stated that the reports based on the comments made by Drogba's friend, who works for the International Channel Shanghai (ICS) would be looked into by the club.
"Regarding the truth of the message left by the ICS journalist, we will investigate it," he said. "There are many rumours and in truth, I felt confused."
Drogba was in attendance with Anelka as Shanghai fell to a 3-1 loss in the 500th game of the club's history against Changchun on Saturday amid continuing speculation.
In Monday's newspapers, however, the Chinese media performed a U-turn. One cited a club official as stating that Drogba would make his return in the match against Dalian Aerbin next Saturday, while Orient Sports Daily quoted Drogba as saying that he had no intention of leaving Shanghai.