All the sources that I looked up indicate that a special prosecutor may be appointed by the judiciary or by Congress.
If we don’t get any names soon, this investigation/ prosecution will go nowhere.
The Ethics in Government Act of 1978 did allow for Congressional and Judiciary involvement but that law had a time limit. It was reauthorized a couple of times but after the Clinton impeachment it was allowed to expire sometime in 1999. I think the Justice Department has a regulation allowing for appointment of a special counsel, such as Patrick Fitzgerald in the Plame matter, but that is up to the Justice Department. If there is any other current authority, I would certainly be interested in knowing about it.