WASHINGTON—Former Massachusetts Gov. Mitt Romney “is under active and serious consideration” to be Donald Trump’s secretary of state, Vice President-elect Mike Pence said Sunday, a move that would moderate the direction of the president-elect’s national security team inside a rapidly expanding administration.

Mr. Trump’s remaining high-profile selections include the economic team that will join him at the White House. He continues to press for J.P. Morgan Chase & Co. Chief Executive James Dimon to be the next Treasury secretary,...