An army spokesman could not confirm or deny the report.
"I was informed that the carcass (of the plane) has been found," said Xolani Mabanga. "I will give more information later, when I receive information from the team on the ground."
The plane had reportedly left Pretoria for Mthatha, a small airport in the Eastern Cape province that is the closest to Mandela's rural homestead of Qunu, where he has lived since retiring from public life.
Rescue helicopters were dispatched to the mountainous region after the plane was reported missing, but had to be called back because of bad weather, reports said.
Ground rescue teams were also sent to the area.