Peaches Geldof , 25, was found dead at her Kent home, on Monday.
In a statement, the council said: “A decision on whether there needs to be an inquest depends upon the final results of the post mortem.”
The council added that it “could take some weeks” for those results.
Peaches Geldof was the second daughter of musician and campaigner Bob Geldof and Paula Yates.
Kent Police said earlier that her death was being treated as “non-suspicious but unexplained and sudden”.
Fifi Trixibelle Geldof paid tribute to her sister Peaches earlier on Tuesday and posted on Instagram: “My beautiful baby sister…. Gone but never forgotten. I love you Peaches x.”
Irish President Michael D. Higgins also paid tribute to the writer, TV presenter and model.
Susan Sarandon, Boy George, politician Martin McGuinness and TV presenter Davina McCall have also offered condolences.
Peaches Geldof’s father Bob said his family are “beyond pain” following the news.
President Michael D. Higgins, who was due to meet Bob Geldof this week during a state visit to Britain, said his thoughts were with the family.
Peaches Geldof had two young sons with her second husband, musician Tom Cohen. She was 11 when her own mother died.
In a family statement issued on Monday night, Bob Geldof said: “She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
“Writing <<was>> destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable?
“We loved her and will cherish her forever. How sad that sentence is. Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken.”
The statement was signed Bob, Jeanne, Fifi, Pixie and Tiger Geldof.
Tom Cohen said: “My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra and I shall bring them up with their mother in their hearts every day. We shall love her forever.”
Bob Geldof was knighted in 1986 for his work in organizing Live Aid and other concerts that raised millions for the starving people of Africa. He first gained prominence as the lead singer of the Irish rock band the Boomtown Rats in the 1970s.
Paula Yates, who was famous for presenting Channel 4’s The Big Breakfast and music show The Tube, died of a heroin overdose in September 2000.
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