The Ivorian striker was linked with moves to both Milan clubs, with Inter Milan emerging as the club that could sign him, and a possible link-up with former Blues boss Jose Mourinho.
However, the 31-year-old has stated he is keen to stay at Stamford Bridge for as long as the club want him, adding that he also hopes to help the club become more successful.
Speaking to Sky Italia, Drogba said, "I believe the future of Chelsea will be splendid because we have created something for which now many want to come to Chelsea.
"They know that when they come here every year they have to fight to win trophies.
"This club was already historical but it will become even more so.
"I am very proud to be part of all of it and I want to stay here as long as they want me.''
Drogba was hampered by injury in the early stages of the season, and suffered loss of form under former boss Luiz Felipe Scolari.
However, since Guus Hiddink took charge at Stamford Bridge, the former Marseille player has improved his form and created a good partnership with Nicolas Anelka.
The player insists however, that he has no bad feelings towards Scolari."I can't be angry with him because it was a choice and the manager's choices should be respected.
"A coach has 22 players at his disposition. He has to make decisions and I think that his weren't bad because Anelka was scoring.
"I couldn't say anything, I had to only wait my turn."
Drogba has recently been charged by UEFA over his comments about referee Tom Henning Ovrebo, after the Blues were dumped out of the Champions League semi-final against Barcelona.
This followed a coin-throwing incident earlier in the season, resulting in the Ivory Coast international receiving a three-match ban.
However, the player has apologised for his actions, and said he regretted both incidents immediately after."Luckily it doesn't happen often to me, but sometimes it happens that you lose control and do something which you regret as soon as the match finishes.''
Drogba also credits Jose Mourinho for his rise to glory with Chelsea.
"Mourinho was very important,'' added Drogba. "When I was playing at Marseille, we came up against Porto and he saw me play.
"Even though they beat us we played a good game, I scored and played well. I think that from that day he sent a scout to follow me in the UEFA Cup games.
"He knew how I was playing and when I had to decide between staying at Marseille or going to Chelsea, he told me 'you are a good player but if you want to become one of the best strikers in the world, at the level of (Ruud) Van Nistelrooy and Thierry Henry, you have to move to a stronger team'.
"Just by saying that he impressed me a lot.
"Then he did a lot for me, when I was going through difficult times he was always there and I paid him back on the pitch. That's why we had such a fruitful relationship.''
Speculation is set to continue over the summer months regarding Drogba's future, despite his recent declaration.
Nick Turner, Goal.com