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The 46-year-old mother of two died in London on Friday after being found unconscious at her living quarters near the exclusive King Edward VI Hospital where she worked.
British media outlets on Tuesday reported that Ms Saldanha left a note for her family - husband Benedict Barboza and children Junal, 17, and 14-year-old Lisha.
The contents of the note have not been revealed.
While on duty as a senior nurse last week Ms Saldanha answered a hoax call from Australian radio jocks Mel Greig and Michael Christian, who impersonated the Queen and Prince Charles as they sought information about a patient, the pregnant Duchess of Cambridge.
Ms Saldanha unknowingly transferred the call to the ward of Prince William's wife Catherine, where a second nurse gave the DJs confidential information about the Duchess, who was being treated for acute morning sickness.
Mr Barboza has called for a thorough investigation into the death of his wife.
Speaking on the family's behalf and with them by his side, British Labour MP Keith Vaz said: "We need to know the facts, fully and clearly. There are unexplained circumstances. The family were in the dark."
Radio station 2Day FM presenters and management, along with hospital representatives and the Duke and Duchess of Cambridge, have conveyed sympathy over Ms Saldanha's death.
Meanwhile a squabble continues as 2Day FM management insist they made numerous attempts to contact the hospital before going to air with the prank call. The hospital denies the claim.
A post-mortem examination was conducted on Tuesday and an inquest into Ms Saldanha's death is likely to be opened and adjourned this week.