Ms Saldanha (46), a mother-of-two, was found hanged in her nurses' quarters three days after she transferred the call from Greig and Christian to a colleague at London's King Edward VII's Hospital who then described the British royal's condition in detail.
Scotland Yard said before Christmas that it had submitted a file to the CPS on December 19 "for them to consider whether any potential offences may have been committed by making the hoax call".
A CPS spokesman said: "It (the file) is still under consideration."
Ms Saldanha left two notes in her room and had marks on her wrist when her body was discovered, Westminster Coroner's Court in London heard as an inquest was opened and adjourned.
Greig and Christian spoke of their grief on Australian television soon after the nurse's death. They said their prank had prompted "a tragic turn of events no one could have predicted or expected".
The Australian Daily Telegraph reported New South Wales deputy police commissioner Nick Kaldas as saying Scotland Yard had not asked for any further information or to interview the two Sydney-based radio hosts.
"Nor do we expect there to be any requests," he told the paper.
"There was some initial contact after the death of Jacintha Saldanha but not a lot since and because of the passage of time we believe it is unlikely any charges will be laid."
Earlier it emerged that Ms Saldanha had made two previous suicide attempts, it has been claimed.
Ms Saldanha was treated in intensive care at a hospital in Mangalore, India, in January, after reportedly falling from a building. It came just nine days after she attempted to commit suicide with an overdose of pills, according to reports.
Those details emerged as Scotland Yard submitted a file and asked prosecutors to consider whether any potential offences were committed by the two Australian DJs.