ROME — Less than two weeks before a potentially tense and diplomatically delicate meeting with Pope Francis at the Vatican, President Trump has apparently settled on nominating Callista Gingrich, the wife of Newt Gingrich, the former House speaker, as the United States ambassador to the Holy See, according to two people close to the president.

The White House did not respond to a request for comment, and the announcement is pending approval from the Office of Government Ethics, according to CNN, which first reported the news on Sunday.

But on Monday, Vincent Salamone, a spokesman for the Office of Government Ethics, which checks for potential conflicts of interest and compliance with financial disclosure rules, said the office “completed its work and cleared her report on April 7.”

That would mean that either another agency in the vetting process had not signed off on Ms. Gingrich’s nomination or that the White House itself did not yet want to make the nomination public.