A post-mortem examination into her death took place on Monday.
No cause of death has been given, while an inquest was opened and adjourned until 26 October. Results of further toxicology tests could take four weeks.
The 27-year-old singer’s body was found on Saturday at her home in Camden, north London.
The spokesman would not reveal any details about the location or time of the funeral.
On Monday, her father Mitch Winehouse thanked fans for their tributes, saying: “I can’t tell you what this means to us. It really is making this a lot easier.”
Visiting his daughter’s home, he added the loss left him “speechless”.
The singer’s mother and brother also visited the site to see the flowers, cards and photos fans laid in tribute.
A family spokesman had earlier said the funeral would be held as soon as possible, with coroners issuing interim death certificates allowing arrangements to be made.
Traditionally, Jewish funerals take place as quickly as possible following a death.
The Brit and Grammy award-winner had struggled with drink and drug addiction for many years and had recently spent time in rehab.
But police have declined to say whether her death was drug-related.
The singer, who topped the charts with her album Back To Black, was found dead by a member of her security team.
The album re-entered the charts on Sunday almost five years after it was released. The record, produced by Mark Ronson, climbed to number 59.
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