Secretary of State Mike Pompeo is still poised to run for an open U.S. Senate seat from his home state of Kansas, according to multiple Republicans familiar with the planning.

Pompeo is not accelerating his plans to leave his current perch and has until a June filing deadline to make a final decision. But any move by Pompeo from Foggy Bottom to the campaign trail will not happen until President Trump signs off on the move, according to one of the Republicans familiar with the ongoing talks, who were all granted anonymity to speak frankly about the matter.

"If Trump realizes that it comes down to Kansas, he'll tell Pompeo to run," that Republican official said.

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At issue is not the impeachment saga engulfing almost everything in Washington. Instead, it's a familiar problem for national Republicans: The party needs a candidate who can win a statewide race.

Kris Kobach, the former Kansas Secretary of State who pushed for some of the nation's strictest voter registration rules, is already in the race to succeed retiring Republican Senator Pat Roberts. Public and private polling shows Kobach would easily win a GOP primary thanks to his conservative credentials, but then lose by big numbers in a general election to a hypothetical Democratic opponent, costing Republicans a critical Senate seat at a time when the chamber is closely divided.

Kobach lost the governor's race last year, an embarrassment for Republicans who gave up the state house as part of the national Democratic wave and Kobach's unpopularity with Kansans overall.

Already, Democratic state Senator Barbara Bollier, a former Republican, is in the race and earning support from national Democrats. There is speculation that Kathleen Sebelius, the state's former Democratic governor who served as secretary of Health and Human Services during the Obama administration, could also join the race.

So, how do Kansas Republicans solve their problem? Enter Mike Pompeo.

Internal Republican polling shows Pompeo to be "incredibly strong" in a potential primary contest against Kobach, according to multiple Republican officials.

"His standing in a primary is astronomical" and it's solid in the general election against a hypothetical Democratic opponent, with Pompeo conceivably winning by at least 20 points, said one of the officials.

"Pompeo has Trump-like numbers in Kansas," that official added.

Another GOP official said: "Every indication I have is that a Senate run is still very much on the table. He would still be, by far, the best candidate." This official added that "the data has shown consistently" that Pompeo would easily win the Senate seat.

The issue is so critical for Republicans that Senate Majority Leader Mitch McConnell — always sensitive to maintain his grip on the Senate — has explained the matter to Mr. Trump, the Republican officials said.

But Mr. Trump doesn't want his Secretary of State to leave town.

"The Pompeo-Trump relationship is still strong," said one of the Republicans.

Traveling in Brussels on Wednesday, aides to Pompeo once again had to tamp down speculation that the secretary is stepping down soon in order to dodge the ongoing impeachment mess in Washington.

State Department spokeswoman Morgan Ortagus told reporters traveling with the secretary that reports of his imminent resignation to run for the Senate are "completely false. He is 100 percent focused on being President Trump's Secretary of State."

Another person close to the secretary said Wednesday that he "is only focused on executing President Trump's foreign policy goals and completing the mission for the American people at the State Department. Anyone who says otherwise is just wrong."