The Los Angeles Times reported her body was discovered at the bottom of a ravine early Tuesday by searchers in Beachwood Canyon. Her Labrador retriever was found alive and sitting beside her, the newspaper said.
Friends had contacted the authorities when Menke failed to return home Monday after a hiking trip.
Sources familiar with the case told the Times they believe Menke became disoriented and collapsed, and that weather conditions contributed to her death.
The coroner's office said no cause of death had been determined, but added investigators were looking at whether Monday's high temperatures were a factor.