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Drogba is under contract with Chelsea until the end of the 2011-12 campaign and he would love to extend his stay at Stamford Bridge beyond that deal.
The 32-year-old, who was the Premier League's top scorer last season as Chelsea won the title, loves living in London and feels it would be too disruptive for his family to move now when they are settled in the English capital.
"I'd love to stay at Chelsea - that is what I'm trying to do," he told the News of the World.
"It is good for me - this is the first time I have stayed so long in a club and everything is made for me to stay and end my career here.
"The family is settled here, the children love it at their schools and it would be very difficult to change them from this place.
"Everybody is happy here. I like London a lot and, if I miss something, I can still nip back to France."
Drogba also played down talk that Chelsea's ageing squad may be too old to dominate English football for much longer.
The likes of Drogba, Frank Lampard and Nicolas Anelka are all over 30, but the striker insists their fitness is as good as ever.
"People mention that we are an old side, but being 32 or 33 now is not the same as being 32 or 33 ten years ago," he said.
"Things have changed a lot and a professional football player now has a very good life in terms of health and training. There are a few more years in me and this team."
However, Drogba has not been fully fit recently following a bout of malaria and he admits it will be another two weeks before he is back to his best.
"It's not nice for me to be on the pitch and not feel 100 per cent, not be able to give what I was giving at the beginning of the season and last season," he added.
"But the important thing now is to get back to that form. Sure, it has been a bit frustrating because I've had fever and colds.
"I've been sweating, been sick for four weeks. In a couple of weeks, I should be back at full strength."