Mr. Romney “would be a terrible choice,” said former Texas Republican Party Chairman Tom Pauken. “His foreign policy views are in total conflict with Trump’s. He will bring terrible people with him to State. His selection will do Trump much more harm than good with Trump’s supporters. It sends exactly the wrong signal.”

The former Massachusetts governor and 2012 Republican presidential nominee criticized Mr. Trump sharply during the campaign and has said relatively little about where he comes down on policy disputes between the Republican internationalist old guard and the “America first” revolutionists whom Mr. Trump championed.

“Romney would hire all those who brought us the Iraq War, Libya and drone-bombing Africa,” Mr. Pauken said. “And he would deeply demoralize Trump supporters.”

Anthony Salvia, who served in the State Department under President Reagan, predicts there would be no rhyme or reason to a Romney-run foreign policy.