"The next step is going to be an interesting one and I think soon I'm going to announce it," Drogba, on his first visit to India for a promotional event, told the moderator of a packed news conference on Sunday.
"For now, I'll just ask you to wait a few moments."
Organisers of the news conference would not take questions from reporters on Drogba's move.
Shanghai Shenhua coach Sergio Batista has confirmed the Chinese Super League club was negotiating with the prolific 34-year-old Ivory Coast international.
"There is a big possibility he will come [to Shenhua] but it will depend on the hard work the club puts into bringing him here," the former Argentina coach said on Thursday.
Tightlipped about his future, Drogba, however, spoke fondly of his days in Chelsea and his decision to leave the club on a high, having scored the winning penalty in last month's shootout victory over Bayern Munich in the Champions League final.
"I took my decision after the Champions League. I took my time because I didn't want to take a too quick decision," he said.
"It was important for me to achieve what I did in Chelsea. I have been the top scorer twice. Winning the Champions Trophy, winning the Premier League...I won everything and I'm proud. It's good to go out at the right time and I think it was the right time."
Drogba looked almost in a trance as he recalled slotting home the decisive penalty in the Champions League final shootout.
"The scenario was like from a movie by [Alfred] Hitchcock, you know, a lot of different emotions," he said.
"It was like a lottery. When I had the chance to score the goal, I went through different emotions from the time I started walking to the penalty spot.
"Many things came to my head but I tried to stay cool and score for my friend Peter Cech who had been amazing that day, saving three penalties."
That victory in Munich's Allianz Arena also meant Roberto Di Matteo would remain the most memorable Chelsea manager, said Drogba.
"We have had so many managers and all of them brought something special to Chelsea. All of them I think were part of our success," Drogba said when asked to name the best manager he has played under at Stamford Bridge.
"When [Jose] Mourinho came, he built up the spirit that we kept all these years and when Carlo Ancelotti came, he also brought another way of playing and thinking. So it's difficult to choose one.
"The one who would be remembered most I think is Roberto Di Matteo for winning the Champions League. The club was waiting for that."
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