The Ivory Coast forward received the 2015 Football Writers' Association Tribute Award at a gala dinner in London on Sunday night.
Drogba returned to Stamford Bridge during the summer following spells with Shanghai and Galatasaray, but as yet there is nothing confirmed when his current one-year deal expires.
However, the 36-year-old indicated his plans very much remain with Chelsea, either on or off the pitch.
"When you have achieved so much and won so many trophies like we have done in the past 10 years, that creates something special," said Drogba, who was unable to prevent Chelsea being knocked out of the FA Cup, beaten 4-2 at home by League One Bradford on Saturday.
"I hope, and the club makes me believe, I am part of this big family, so we are going to find the best thing for both of us to promote the club in the best way."
Drogba added: "When I left this club (the first time), I was saying that I had done everything I wanted to do, but I think now that I did not do everything, I think there is more to do.
"I love this club and would love to be part of this club for the future, with the new players."
Barclays Premier League leaders Chelsea will look swiftly to put the defeat by Bradford behind them when they host Liverpool for Tuesday night's second leg of their Capital One Cup semi-final, which is poised at 1-1.
Drogba said: "Everybody was disappointed and of course we are not proud of what happened, but the good thing is in two days we have another game, so we have to focus on this game and try to play better than we did at the weekend."
England manager Roy Hodgson was among the guests at the Savoy Hotel to hear tributes to Drogba from current Chelsea team-mate Petr Cech and former Arsenal striker Thierry Henry.
Drogba added: "I am really proud for this award, in the list of previous winners there are a lot of players whom I really respect and grew up trying to reach there level, so for me this is a great honour.
"When I came to England, things were difficult, there was the language barrier and culture change.
"With time, we managed to learn more from each other and today I am really happy that the football writers not only understand me a lot on the pitch, but have also helped me with my foundation work."
Chelsea manager Jose Mourinho, who first signed Drogba from Marseille for Â£24million in 2004, wrote a personal tribute to the striker in the FWA event programme.
Mourinho wrote: "Throughout my career, I have always refused to say which is my favourite player or the best person, because so many have given soul and blood to play and to fight with me, but if I have to choose one who represents all the good things you want in a player and a man, I think in this moment I would choose Didier."
Source : PA