The 33-year-old is believed to have been undergoing contract negotiations over a new deal with the former Premier League champions in recent months.
With no news of a fresh contract, speculation has surrounded the Ivorian, who is currently on international duty in the Africa Cup of Nations.
While Chinese outfit Shanghai Shenhua have claimed that they are close to clinching the frontman, Drogba has stated his intentions to remain in London.
"I would like to find again more fun, shivers, fervour, pressure and passion on the pitch," Drogba told France Football. "That makes fun in our job and I have missed a little for the last months. Does it mean departure from Chelsea? Not before next June."
It is thought that the forward is keen on a two-year extension with Chelsea.