Memphis police tweeted this morning that “a deceased party” had been found in the same area.
“The identity of this person and the cause of death is unconfirmed at this time,” police said.
“The investigation is ongoing.”
Fletcher, 34, was jogging at about 4am Friday local time when she was attacked and forced into an SUV, police say.
They had previously said she may have been seriously injured in the kidnapping.
Although Fletcher is still missing, police have charged a man over her disappearance.
US Marshals arrested 38-year-old Cleotha Abston on Saturday after police detected his DNA on a pair of sandals found near to where Eliza Fletcher was last seen, according to an arrest affidavit.
Police also linked the vehicle they believe was used in the kidnapping to a person at a residence where Abston was staying.
Fletcher is the granddaughter of the late Joseph Orgill III, a Memphis hardware businessman and philanthropist.
The family has released a video statement asking for help in finding Fletcher and offered a $73,500 reward for information in the case.
