U.S. Supreme Court building in Washington, D.C. Janhvi Bhojwani | CNBC

This will be a double-secret discussion. The justices of the Supreme Court on Friday will discuss whether to allow a mysterious foreign-owned company to file — without the public seeing it — to ask that the high court hear its challenge of a subpoena that is suspected to have been issued at the request of special counsel Robert Mueller. If the justices approve that bid, it then could possibly set the stage for a rare, if not unprecedented scenario: the Supreme Court being asked to hear oral arguments in a case without the public being able to witness them. But if the Supreme Court rejects the company's request at the justices' conference on Friday, the unidentified company could still ask the high court to hear its appeal, albeit with a filing of documents that would be open to the public.

However, even if the company chooses that route, the Supreme Court is not obligated to grant the request to the case, which is known as a petition for a writ of certiorari. By the time that the justices meet on Friday, the company will have racked up more than $500,000 in fines for not complying with the subpoena. Walter Dellinger III, an appellate lawyer who as acting solicitor general argued at the Supreme Court for the government of the United States from 1996 to 1997, told CNBC, "I know of none," when asked whether he had heard of any prior case in which the high court considered a request to be heard on appeal in sealed documents. Dellinger also said he was unaware of the Supreme Court hearing a case in a session closed to the public.

A case shrouded in secrecy