Secretary of State Mike Pompeo says he isn’t running for Senate next year. Those close to him say he hasn’t made a final decision yet. But that hasn’t prevented a barely concealed competition from breaking out within the administration over who might replace him as the nation’s top diplomat. President Trump has fueled the fire by sounding out lawmakers and officials as he considers his options.

Pompeo has plenty of time to decide whether to run before the official filing deadline in June. Senate Majority Leader Mitch McConnell (R-Ky.) is pushing him hard to jump into the Kansas Senate race, several officials and GOP lawmakers told me, out of fear former Kansas secretary of state Kris Kobach might win the primary and then lose the general election to a Democrat. Pompeo is also mulling a run for president in 2024, and McConnell has argued the Senate would be a perfect perch from which to do that.

Trump said last month that Pompeo came to him and told him he wanted to stay. But Trump also hedged by saying that if there’s any danger the GOP could lose that seat, Pompeo might change his mind and “would win in a landslide because they love him in Kansas.” Pompeo himself, meanwhile, is sending mixed signals. This month he began posting from a new personal Twitter account with Kansas farmland in the banner photo.

All this uncertainty has caused several officials to quietly begin to position themselves for the secretary of state job. Trump, not knowing how it will turn out, has been tossing around names for Pompeo’s successor with lawmakers and officials, according to three people who spoke with him directly about it. Speculation is heating up all over the administration.

The person most often mentioned to succeed Pompeo is national security adviser Robert O’Brien. Trump really likes O’Brien, several officials told me, and has given him increased diplomatic responsibilities since he became the president’s fourth national security adviser in September. O’Brien stood in for Trump at the Association of Southeast Asian Nations summit in Thailand in October. He accompanied Vice President Pence and Pompeo to Turkey to negotiate a Syria cease-fire.

Pompeo is also a big fan of O’Brien, who worked for Pompeo as special presidential envoy for hostage affairs before he moved to the White House. O’Brien is known as a competent, polished technocrat who works well with all the various administration factions — which is rare.

The other main contender at this point is Treasury Secretary Steven Mnuchin. Some officials believe Mnuchin is angling for the job, and some say he is simply in contention but not actively lobbying. Either way, he’s on the list. Mnuchin is very close to Trump personally and has been treasury secretary for almost three years.

But many national security officials are concerned that Mnuchin’s dovish position on China and his Wall Street focus could undermine his fitness to lead U.S. diplomacy. He recently delivered Trump the phase one China trade deal but has consistently resisted the more hawkish China strategy supported by Pompeo, Pence, O’Brien and most of the administration.

He would have a confirmation problem, too, having only narrowly been confirmed for his current job, 53 to 47, amid concerns among Senate Democrats about his overall lack of experience. Also, though Pompeo and Mnuchin are political allies, they disagree on foreign policy. O’Brien would represent continuity, whereas Mnuchin would represent a stark departure from the status quo at State.

Trump has also asked people what they think about Ambassador to Germany Richard Grenell becoming secretary of state. The German government has complained about Grenell’s aggressive style, but that’s actually a selling point for Trump. Grenell’s confirmation would also be tough; he was confirmed for his current job by a vote of 56 to 42. O’Brien and Grenell have been friends for many years. They were both acolytes of former national security adviser John Bolton.

Newly minted Deputy Secretary of State Stephen Biegun would become acting secretary of state, at least for a while, if Pompeo departs. Depending on when Pompeo steps down, it might be too late for Trump to get someone new confirmed, leaving Biegun in charge at Foggy Bottom until the election. Biegun is said not to be seeking the job full time, but he’s on Trump’s list.

The other names often mentioned are State Department envoy to Iran Brian Hook, who has a close relationship with Jared Kushner, as well as Sens. Marco Rubio (R-Fla.) and Tom Cotton (R-Ark.). Hook is seen as unlikely to ultimately get the nod because he has some detractors among Trump’s allies. Rubio and Cotton both have presidential aspirations, and a stint as secretary of state could only help them.

That brings us back to Pompeo, who is keeping us all in suspense. Does he really want to go from being secretary of state to a position as the junior senator from Kansas? If he is going to run for president on his diplomatic record, might he not want to stay another year and finish the job?

If so, this entire contest will simply be shelved until Trump’s second term (should he be reelected). But until everyone else can be convinced that Pompeo is definitely staying, the competition for his job will keep heating up.

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