The body was not immediately identified and no cause of death has been determined, according to a police news release.
Forty-year-old Gerrie Lawrie was reported missing Saturday by former Shelby County Sheriff Gene Barksdale, who had spent time with her while she was in Memphis for activities last week on the anniversary of Presley's death, according to The Commercial Appeal (http://bit.ly/n73vju ).
Officers said there were no obvious signs of foul play, but they were still investigating.
Memphis acquaintances told the paper this was Lawrie's sixth visit to Memphis and that she wanted to move to the city where Presley spent much of his life and died. It's also home to his Graceland estate.
Lawrie did not fly home to Aberdeen, Scotland, as scheduled, the paper said.
Barksdale said he had not seen Lawrie since escorting her to her rented vehicle in a downtown parking garage last week. The paper said he walked with her to a second story, where her vehicle was parked, and she gave him a lift back to his.
The ex-sheriff, 89, told the paper that Lawrie works for an oil company in Scotland.
John Helms, a Memphis artist who said he has helped act as a host during her visits, said she has not answered his attempts to reach her by email, cell phone and the Skype Internet service.
"Either she has turned off communication or else someone has for her," Helms told the paper.
Police said the person was dead at the scene at a city address. They did not say in their news release whether an autopsy would be done.