President-elect Donald Trump is leaning toward asking former Massachusetts Gov. Mitt Romney to be his secretary of state, according to people familiar with the deliberations.

The next U.S. president is also likely to name retired Marine Gen. James Mattis to serve as secretary of defense in his administration, and South Carolina Gov. Nikki Haley was picked to serve as the U.S. Ambassador to the United Nations, two people familiar with the matter said, awarding the rising Republican star with a key diplomatic post. And former...