The note will provide a critical insight into Ms Saldanha's death at her inquest, which was due to open this week but has been delayed.
It had been reported Ms Saldanha criticised the hospital for her treatment after the prank call.
The note is reportedly one of three which Ms Saldanha wrote before she died.
Another says she did not blame her work colleagues for the distress she felt. The third left instructions for her funeral.
Southern Cross Austereo, which owns the Sydney radio station, has said it would contribute A$500,000 ($600,000) to a trust fund for Ms Saldanha's family.
Ms Saldanha, who shared a home in Bristol with her husband, Benedict Barboza, 49, a hospital accountant, and their two children, Junal, 17, and Lisha, 14, had trained as a nurse in Mangalore, southern India, before moving to Britain more than a decade ago.
It was revealed that she was upset by problems she was having at work and Mr Barboza criticised the hospital for its handling of the situation.
It has also emerged that she had previously been placed on antidepressants.
According to the Sunday Times, Ms Saldanha had previously been in hospital in India for depression, although her family claims this was because of an accident.
A source close to the case said her discharge note from the Indian hospital said she would need to be monitored 24 hours a day because she had high suicidal tendencies.
The newspaper said her employers were never told this.
A spokesman for King Edward VII's Hospital said: "Jacintha Saldanha was an outstanding and much-loved member of our team. We continue to assist the coroner so that she can establish the full facts of the case."
Keith Vaz, the Labour MP who has acted as Ms Saldanha's family's spokesman, said: "The forthcoming inquest will hopefully provide answers for the family and for them it will represent closure."
* If it's an emergency and you feel like you or someone else is at risk, call 111. Or call Youthline 0800 376 633, Lifeline 0800 543 354, Depression Helpline 0800 111 757, What's Up 0800 942 8787 (noon-midnight).
- AAP