They were the types of meetings more typical for a political candidate than for the nation’s top diplomat.
But on a trip to New York on Tuesday, Secretary of State Mike Pompeo got together with Ronald S. Lauder, the cosmetics heir and billionaire Republican donor, two people briefed on the meeting said, speaking anonymously 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 only gave 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.
People close to Mr. Pompeo declined to comment on his intentions, saying only that he was “focused” on his role as secretary of state.
At the State Department, officials described widespread belief that Mr. Pompeo was on his way back to the American heartland. One senior American official referred to the speculation as reaching a “fever pitch.” Another recently retired senior official said it was widely believed that Mr. Pompeo would leave soon — assuming he navigated his exit with Mr. Trump’s blessing.
In television interviews on Tuesday, Mr. Pompeo said he had no immediate plans to run for Senate. “I’m going to be the secretary of state as long as President Trump continues to want me to be his secretary of state,” Mr. Pompeo told CNBC’s “Squawk Box.”
Asked what he would say if Mr. Trump urged him to run for the Senate, Mr. Pompeo answered, “He and I’d have a serious conversation.”
But, he continued, “I’m so focused on what I’m doing. I hear all the chatter; I see it. I think the only one not talking about my Kansas Senate run is me.”
The filing deadline to run for the United States Senate seat from Kansas is not until June 1. The incumbent, Pat Roberts, has announced he is retiring. But Mr. Pompeo’s recent travels to Kansas, where he once served as a congressman — and an upcoming Sept. 6 speech at a Kansas State University lecture series — have increased speculation about his plans.
Democrats ran strongly in heavily Republican Kansas last year, winning the governorship, and Republicans are concerned that they could lose the Senate seat if the party’s nomination goes to Kris Kobach, a divisive conservative hard-liner.
Mr. Pompeo was Mr. Trump’s first C.I.A. director and took over the State Department in April 2018. His leadership of the diplomatic corps has not been as volatile as that of his immediate predecessor, Rex W. Tillerson, who cut the department’s budget, in part by shaving staff positions.
But Mr. Pompeo is not viewed at the State Department as having broadly advanced foreign policy beyond his attention to cracking down on Iran.
Mr. Pompeo did not directly address his possible candidacy at the lunch with the conservative group on Tuesday, instead focusing on the administration’s policy toward China.
“I have confidence Secretary Pompeo has a firm handle on the issues affecting us on the global stage,” Mr. Catsimatidis’s son, John Catsimatidis Jr., said in an interview after the event.