New South Wales Police said they were in contact with London's police force and were ready to assist in any investigation, as the incident sparked fresh soul-searching over the behaviour of the media.
Jacintha Saldanha, 46, was found dead in staff accommodation near London's King Edward VII hospital on Friday after putting the hoax call through to a colleague who unwittingly disclosed details of Kate's morning sickness to 2DayFM's presenters.
A recording of the call, broadcast repeatedly by the station, rapidly became an internet hit and was reprinted as a transcript in many newspapers.
Public amusement at the prank turned to disgust after news of Saldanha's death swept around the globe. The station's owners pulled presenters Michael Christian and Mel Greig off the air as leading companies cancelled advertising.
The station's parent company, Southern Cross Austereo (SCA) , said it would fully cooperate in any investigations in a letter to the head of the King Edward hospital.
"I can assure you we are taking immediate action and reviewing the broadcast and processes involved," SCA chairman Max Moore-Wilton said.
"We are all saddened by the events of the last few days. They are truly tragic... The outcome was unforseeable and very regrettable," he added.
The station's presenters have come under attack from around the world on social media sites and were "extremely distressed", an SCA spokeswoman said.
Both were keen to speak publicly about the incident, but were in too fragile a condition to do so, the spokeswoman added.
The hospital's chairman Lord Glenarthur had described their actions as "appalling" in a letter to SCA on Saturday.
Saldanha, married with two children, was originally from India and came to Britain around 10 years ago.
Her husband's family in the southern Indian state of Karnataka said she had spoken regularly to them but neither she or her husband had mentioned the hoax call, they told Britain's Observer newspaper.
A post mortem into the cause of her death will be held early next week, possibly as soon as Monday. An inquest will follow, and London police may want statements from the two presenters, although they had yet to make a formal request.
"It's been indicated that the London Metropolitan Police may wish to speak to the people involved in the matter from 2DayFM," said New South Wales Police Deputy Commissioner Nick Kaldas.
"But we haven't been asked to do anything yet, and we certainly have not been asked to interview anyone, or line up any interviews for the Met," he added.
The tragic fallout from the radio stunt has rekindled memories of the death of William's mother Diana in a Paris car crash in 1997 and threatens to cast a pall over the birth of his and Kate's first child.
The couple's baby will be third in line to the British throne after William and his father Prince Charles.
The royal family are enjoying a boost in popularity in Britain after a period when they were seen as dated and out of touch.
William and Kate's wedding at London's Westminster Abbey last year rekindled public enthusiasm for royalty, which has been sustained during this year's jubilee celebrations for Queen Elizabeth's 60 years as monarch.