The device was found in a garden bed near a security car that was monitoring Kidman's home from the street, chief bodyguard Neil McMaster told Sydney's The Daily Telegraph for its Tuesday edition.
He said he believed the device was intended to intercept conversations among the actress and her bodyguards.
Police have released closed circuit video footage showing a man crossing the street near where the security men gather.
"Police are examining some surveillance footage that has been given to us. That footage captures a man who was in the near vicinity of where this device was," said Detective Inspector Grant Taylor of the New South Wales Police. "We are currently enhancing that video footage, and we hope that the man in that footage will assist us with our enquiries."
It was apparently discovered when security officers searched the house early Sunday in preparation for Kidman's return to film her new movie, "Eucalyptus."
Police were called and seized the device for forensic examination, a News South Wales state police spokeswoman said on the usual condition of anonymity.
If identified, the eavesdropper could be charged with illegal use of a telecommunications device and trespassing. The penalty in New South Wales for bugging someone is between two and five years in jail.
Nicole Kidman's father, Tony Kidman, a psychologist, said he would be very pleased if people would "just let her get on with her life."
"She's concerned that people will not let her alone, and she's here to make a film," said the senior Kidman. "She wants to promote Australia and she's almost a prisoner in her own house as a result of the people who pursue her for pictures and so on."
Kidman has been pursued by eavesdroppers in the past - paparazzo Eric Ford recorded a telephone conversation in 1998 between Kidman and her then-husband Tom Cruise and sold it to the U.S. supermarket tabloid newspaper The Globe.
The 37-year-old actress won a best-actress Oscar for her role in 2002's "The Hours." She has also won best-actress Golden Globe awards for "The Hours," "Moulin Rouge" (2001) and "To Die For" (1995).
She has several films slated for release in 2005, including a big-screen version of the television series "Bewitched," co-starring Will Ferrell.