A question has loomed over Washington: What will the special counsel, Robert S. Mueller III, do when he wraps up his investigation into whether the Trump campaign conspired with Russia and whether President Trump obstructed justice?

The leading theory is that Mr. Mueller will write a report for his supervisor at the Justice Department. That could lead to a new fight: Mr. Trump’s lawyer, Rudolph W. Giuliani, has suggested that the White House may then invoke executive privilege and order the Justice Department to keep portions of such a report confidential from Congress.

But there is historical precedent for another model. Echoing a move by the Watergate prosecutor in March 1974, the grand jury with which Mr. Mueller has been working could try to send a report about the evidence it has gathered directly to the House Judiciary Committee. And on Friday, seeking to draw more attention to that option, three prominent legal analysts asked a court to lift a veil of secrecy that has long kept that Watergate-era report hidden.