Mr. Mueller could take pages from the playbook of Leon Jaworski, the Watergate prosecutor. If Mr. Mueller finds evidence of wrongdoing by Mr. Trump, he could try to use the grand-jury process to make the information public or disclose it to Congress. Mr. Mueller could name Mr. Trump as an unindicted co-conspirator in charges that are filed against others.

Like Mr. Jaworski, Mr. Mueller could also ask the grand jury to send a report about Mr. Trump’s actions, and supporting evidence, to the House Judiciary Committee. But Mr. Mueller would have to get Mr. Rosenstein’s permission for either or both steps.