According to Eyewitness News, there were plans to move the 94-year-old from the facility to his Houghton home on Thursday, but doctors decided to keep him for one more night.
Local and international media have been camped outside the 1 Military Hospital in Pretoria since news of his hospitalisation last Saturday. Until Thursday evening, it was widely believed that Mandela had been at the hospital but the presidency declined to confirm it.
EWN reported that Mandela was not at the Military 1 Hospital and was at a private facility which was known to them.
"The name of the hospital is known by Eyewitness News, but this is not being released to respect Madiba's dignity," it said on its website.
"Several staff members... have confirmed that he has received several visitors (including) former president Thabo Mbeki, Madiba's wife Graca Machel, and Winnie Madikizela-Mandela."
Mandela was receiving treatment for a recurring lung infection.