Jacintha Saldanha, 46, was discovered on Friday morning in her room at staff accommodation near the London's King Edward VII Hospital, which was treating Kate Middleton.
"Initial official statements suggested that she was alive but unconscious when she was discovered, however it is now understood she was found dead," Sky News reported.
The death is not being treated as suspicious. The results of the post-mortem examination are not yet known, and an inquest is due to be opened and adjourned on Thursday, the report said.
The cause of Saldanha's death will not be released until a Westminster Coroner's Court hearing, Scotland Yard said on Wednesday.
The mother-of-two was found dead days after an Australian radio station duped staff at London's King Edward VII Hospital into revealing details of the Duchess of Cambridge's condition, who was being treated for severe morning sickness.
Two presenters - Mel Greig and Michael Christian - on Sydney's 2Day FM radio station called the hospital while impersonating the Queen and Prince Charles.
Saldanha, who took the call, transferred it to the ward where Kate was being treated. A second nurse then divulged details of Kate' condition.