The Ivory Coast striker is in the final year of his contract in West London and the Blues are thought to have offered him a 12-month extension on his deal.
However, 33-year-old Drogba is believed to want two more years, with a view to hanging up his boots at the Premier League club.
Uncertainty has surrounded his future since the ?50million arrival of Fernando Torres from Liverpool in January, with the hitman no longer guaranteed a starting spot in manager Andre Villas-Boas' line-up.
But Drogba maintains he is going nowhere while he is still under contract, and hopes the situation will be resolved.
He told the Sunday Mirror: "I said a few years ago that I will be here until the end of my contract. But I would like to finish my career here. We are continuing talks.
"Everybody knows what I feel about Chelsea and what I want."
Villas-Boas says the situation is still up in the air, adding: "He knows our offer and he has made a counter offer.
"We are now waiting on things."
Source: Team Talk
Source: Team Talk