Republican presidential nominee Donald Trump, left, has named Kansas Gov. Sam Brownback, right, to an advisory council of prominent Catholics.

A top official in the Kansas Republican Party fueled speculation Wednesday that Gov. Sam Brownback could be chosen for a job in President-elect Donald Trump’s administration.

Clay Barker spoke as part of a panel discussion at the Dole Institute of Politics Wednesday that focused on analyzing the results of the 2016 state elections in Kansas.

But the conversation frequently drifted into the presidential race, and in particular the impact it could have on the future of politics in Kansas.

Clay Barker, executive director of the Kansas Republican Party, sparked new speculation Wednesday that Gov. Sam Brownback may be chosen for a position in the incoming Trump administration.

“I have no inside information about the nominations,” Barker said. “But someone on the Trump team told me that there are positions, I have no idea which ones, that if Gov. Brownback wanted them, he could have them.”

Brownback has been mentioned in national news reports as a possible candidate for U.S. Secretary of Agriculture. But there has also been speculation that he could be a possible candidate for an ambassadorship.

Brownback himself has declined to comment on that speculation.

“I’m just making no comments about anything regarding the Trump administration,” Brownback told reporters Tuesday.

Part of the Kansas political world has been changed already with Trump’s nomination of U.S. Rep. Mike Pompeo of Wichita to be CIA Director. If he is confirmed, as most observers think he will be, that would prompt a special election to fill his congressional seat.

Already, several high-profile Republicans from the Wichita area have expressed interest in that seat, including State Treasurer Ron Estes.

In addition, Trump last week interviewed Kansas Secretary of State Kris Kobach, who was photographed going into the meeting holding a document that was labeled a “strategic plan” for the Department of Homeland Security.

If Pompeo resigns his seat to accept the CIA post, it would be filled by a special election that would likely take place in February or March. But the governor would make appointments to fill vacancies in state offices of Treasurer or Secretary of State.

If Brownback is also selected for an administration job, however, his office would fall to Lt. Gov. Jeff Colyer, which could raise questions about conflict of interest because he is also a plastic surgeon and a partner in a Johnson County medical practice.

The last time a Kansas governor resigned to take a job in a new presidential administration was 2009, when then-Gov. Kathleen Sebelius, a Democrat, resigned to become Secretary of Health and Human Services in President Barack Obama’s administration.

Brownback was first elected governor in 2010 and was re-elected in 2014. The Kansas Constitution limits governors to serving no more than two consecutive four-year terms, so he cannot run for re-election as governor again in 2018.

Much of the discussion at the Dole Institute’s post-election conference focused on Brownback and the impact he had on the 2016 state legislative races, when conservatives allied with him lost eight seats in the Kansas Senate, and 13 more in the House.

Several people on the panel said they thought the election was a referendum on the Brownback administration.

“Gov. Brownback’s approval rating over 10 polls is about 22 percent,” said Bob Beatty, a political science professor at Washburn University in Topeka.

“Keep in mind folks, this is the worst approval rating of any governor in the nation,” he added, “and we’ve had two governors, one in Maine and one in Alabama, who are embroiled in ridiculous scandals. So this is a scandal-free governor at 22 percent.”

Some on the panel noted that Brownback has accomplished nearly every policy goal he had hoped for when he first ran in 2010. And while those policies, including the sweeping tax cuts he championed, may not have worked out as planned, there may not be much left for Brownback to do as governor, especially with a more moderate Legislature coming in for his final two years in office.

Barker, however, said he thinks Brownback could remain a significant force in the Statehouse, if he chooses to stay.

“Sam Brownback, whether you like him or not, is one of the most successful politicians in Kansas history,” he said. “Five statewide victories (three as U.S. senator and one as governor). He’s worked with different legislatures and I think he’s going to be open to different solutions.”