The Sunday Mirror quoted Janis Winehouse as saying she believed it was "only a matter of time" before her daughter died. The 27-year-old singer was found dead at her London home on Saturday.
"She seemed out of it. But her passing so suddenly still hasn't hit me," Janis Winehouse told the tabloid.
Ambulance crews were called to the singer's home in north London's Camden area Saturday afternoon. Paramedics found her dead before they arrived.
Police said the cause of her death is being treated as "unexplained," rejecting speculation that she died from a drug overdose as "inappropriate." A post-mortem is expected Monday or Tuesday.
The singer's family said in a statement it was remembering her, and request for privacy.
"Our family has been left bereft by the loss of Amy, a wonderful daughter, sister, niece. She leaves a gaping hole in our lives," the statement said.
Fans from around the world and neighbors have left a growing pile of flowers, candles and messages outside Winehouse's home, as tributes from celebrities poured in. One of the messages read "R.I.P. Never Forgotten," while another said "It's all right, love. Go now."
The Associated Press contributed to this report.