A statement on David Bowie's official Facebook page says his family is planning a private ceremony to remember him as British media report the singer has already been cremated quietly in New York without his friends or family in attendance.
Reuters could not confirm the reports and Bowie's representatives did not return requests for comment.
The British rock star died from liver cancer on Sunday, his music producer Tony Visconti has revealed.
Bowie's family thanked fans for their support on the Facebook page but repeated requests for privacy.
"The family of David Bowie is currently making arrangements for a private ceremony celebrating the memory of their beloved husband, father and friend," the family's statement said. It was dated from England but gave no details about where or when the ceremony might take place.
"They ask once again that their privacy be respected at this most sensitive of times. We are overwhelmed by and grateful for the love and support shown throughout the world."
Bowie's death after a secret 18-month battle with liver cancer and two days after releasing a new album caused shock and dismay around the world and sent sales soaring of both his old and new music.
The album Blackstar, now seen as Bowie's self-styled epitaph, is expected to top music charts in Britain and the United States next week.
US Sales of Blackstar increased 1055 per cent once the news broke of his death, according to Nielsen.
Radio airplay increased 1134 per cent from Sunday to Monday, at Nielsen Music-monitored US terrestrial radio stations, it added.
While fans and commercial enterprises have planned tributes and concerts for Bowie, including one in New York's Carnegie Hall in March, his family said on Thursday that "none are official memorials organised or endorsed by the family".
"Just as each and every one of us found something unique in David's music, we welcome everyone's celebration of his life as they see fit," the statement added.
Bowie is survived by his wife of 24 years, model Iman, adult son Duncan Jones from his first marriage, and teenage daughter Alexandria.
