They were the types of meetings more typical for a political candidate than for the nation’s top diplomat.

But on a trip on Tuesday to New York, Secretary of State Mike Pompeo met with Ronald S. Lauder, the cosmetics heir and billionaire Republican donor, two people briefed on the meeting said, speaking on the condition of anonymity to describe a closed-door gathering. He then met with a conservative group, the Committee to Unleash Prosperity, which routinely hosts events with prospective candidates. That meeting included Steve Forbes, the chairman of Forbes Media; the economist Arthur B. Laffer; and John A. Catsimatidis, a former New York City mayoral candidate.

Mr. Pompeo’s itinerary gave only more credence to the regular talk in Washington that Mr. Pompeo was seriously weighing a run for Senate from Kansas, a step favored by Republicans worried about holding the seat next year but one that would leave a hole in the top ranks of President Trump’s national security team.