The unit has been without a permanent head for over a year after Judge Willem Heath resigned in 2011.
The Presidency on Monday said the matter was still under President Jacob Zuma's consideration.
"The matter is still receiving the attention of President Jacob Zuma. It would be inappropriate to disclose the names of the candidates that are under consideration, in order to protect their privacy as well as the integrity of the process and the institution," said the high office.
Once the President has made his decision, the public will be informed, said the Presidency.
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