(CNN) On a trip to Iowa last week, Secretary of State Mike Pompeo got a tip from his team: the chain supermarket Hy-Vee located on his way to speak at a local high school is a go-to lunch spot for National Guard members.

So on a bitter-cold Monday afternoon, Pompeo and his wife, Susan, warmed up over local grub at the no-frills grocery store. They chatted with locals, including a few National Guard members.

There were no news camera crews and no photos tweeted out by the Secretary or the State Department. But the pit stop, in an important state to presidential politics, had the hallmarks of a political event.

Iowa was just the first of three US states that Pompeo will visit in a matter of a month. Pompeo is in Texas today speaking at an energy conference hosted by Cambridge Energy Research Associates. Next week, he will deliver a speech in his home state of Kansas.

These domestic trips -- notable for a secretary of state whose mission it is to represent the US abroad -- are raising speculation within the administration about Pompeo's future ambitions in 2020 and beyond.

A loyal lieutenant to President Donald Trump, Pompeo is unlikely to be a contender in the 2020 presidential campaign and has publicly ruled out running for an open Senate seat in his home state of Kansas in 2020.

Those who know Pompeo well, however, say that he has political ambitions that extend beyond just the titles of CIA director and Secretary of State: He would also like to be Secretary of Defense and President of the United States.

"Secretary Pompeo's trip to Iowa and soon to be followed by his home state of Kansas, while on government plane no less, has raised eyebrows in the White House and with outside advisers to the President," a senior administration official told CNN.

Each domestic trip Pompeo is making has a different, but official, reason: In Texas he will take part in an energy conference and in Kansas he will speak at a global entrepreneurship summit, topics that fall outside the traditional foreign policy remit.

Asked about Pompeo's domestic travel, Robert Palladino, a spokesperson for the State Department, told CNN, "The first client of the State Department is the American people. The Secretary believes it is important to speak directly to the American people to explain how the work of diplomats around the world contributes to their safety, security, and prosperity."

Pompeo delivered a similar message to the Iowa Farm Bureau last week.

"Many Americans look at the State Department and wonder what it does for them. They see the Secretary travel to far-off places and they ask the question, 'Is America, are Americans, the first client of the State Department?' You should know that you are," Pompeo said.

Pompeo also explained in a tweet that he was in Iowa to recruit diverse State Department employees so that US diplomats reflect the "millions of Americans outside the Boston-DC corridor."

But while traversing Iowa in the frigid weather -- and doing one TV interview outside -- the former congressman from Kansas also got the chance to show Iowans his personable side. Pompeo ingratiated himself with the Midwestern crowds, telling them about spending his childhood summers on a family farm in Kansas.

"They were some of the most special times in my life," Pompeo said during his speech at the World Food Prize event in Des Moines. "George Washington has the famous quote that says, 'I would rather be on my farm than be emperor of the world.' I think he means that, too."

Those who met Pompeo in Iowa told CNN that they could easily envision him being comfortable at the Iowa State Fair and "loving every minute of it."

"He is just really, really smooth. He is also good and reasonable. He can operate up and down the vertical chain from Kim Jong Un, to CEOs of American firms, and employees to boot," a source familiar with the planning of the trip, who was there with him at the majority of the events, said. "It was all upside for him, there was no downside."

Previous secretaries of state have made a concerted effort to explain their work to the American people, without placing too much of a focus on domestic travel.

"Secretary (John) Kerry used to say that there should be nothing foreign to the American people about foreign policy," said John Kirby, a CNN analyst and the former spokesperson at the State Department.

He continued, "That said, domestic travel and speaking never even came close to eclipsing his foreign travel requirements. The essential job of the Secretary of State is to represent the nation abroad and to implement, support and defend American national interests around the world."

Former Secretaries of State Hillary Clinton and Kerry were known for extensive international travel during their tenure. During her first year in the job, Clinton visited 44 countries and Kerry also broke records for miles traveled on the job. After almost a year, Pompeo has already logged visits to 32 countries.

Clinton, who had run for president in 2008 and became a contender again in 2016, also made a number of high-profile domestic speeches as Secretary of State, but the majority of them were in Washington and New York. During her first year she didn't officially travel anywhere nationally outside of the Acela corridor. She did travel to Hawaii and Kentucky during her second year on the job, but as President Obama's chief diplomat she never gave formal remarks in Iowa, waiting until she left the State Department to return to the Hawkeye State.

Many political strategists compare him to any other politician who dreams about being president one day. And Pompeo has managed to do something rare in the Trump era: survive in the administration and not wholly alienate himself from the Republican Party writ large.

"There's nobody in the administration, the Senate or a governor's mansion that it doesn't cross their mind to run for president. They all think about it, the question is whether they pull the trigger or not," says Terry Sullivan, a Republican strategist and former 2016 campaign manager for Marco Rubio. "He (Pompeo) is one of the few people in the administration who looks pretty good right now to all sides."

Pompeo, who now has experience inside and outside government, has maintained a close bond with Trump. This has given the Secretary of State some flexibility and autonomy.

As he explained to high schoolers in Iowa, Trump tells him which "outcomes" to "deliver" on and gives Pompeo and his team a long leash to "implement and execute."

But he also drew some distance in Iowa with the President's politics on trade, where tariffs have created hardship for farmers in the region.

Asked by a high schooler what the plan was to help Iowa famers deal with retaliatory tariffs, Pompeo replied, "Yeah, well, it's the President's plan, not mine."

"But I'm certainly part of it. Look, these are hard fights, but it's not fair," he added.

In addition to speaking with hundreds of Iowans, Pompeo also did six media interviews during the short visit, which is more than he ever does when he travels internationally.

From high school students to fifth generation farmers, Pompeo took questions from the audience everywhere he went. At one point an audience member joked that Kansas would love to have him back. Speculation about Pompeo running for the Kansas senate seat that will be vacated in 2020 with the retirement of Pat Roberts swirled around Washington and Kansas over the last few months. Pompeo even met with a Republican strategist to discuss it.

Weeks after Trump declared that Pompeo was "absolutely not leaving," Pompeo finally declared he had "ruled out" the option. Pompeo sought to nip that idea in the bud, again, when it came up in Iowa.

"Do not start that rumor. You've got media in the back," Pompeo said with a laugh. "There is no upside to that."