The Trump bandwagon is growing quickly as the transition team scrambles to put together a full slate of leaders to fill out the administration and plot an agenda, and is leaving lobbyists on the outskirts.

One transition team member, speaking on the condition of anonymity, said an all-hands meeting just before the election was sparsely attended. Wednesday’s meeting had 10 times more people.

Although some of those leading transition teams on energy or homeland security are lobbyists, most of those in the room are not. Instead, think-tank types from places such as The Heritage Foundation are prominent. That is a break from previous transition teams, where lobbyists have dominated.

“It is very much a nonofficial Washington crowd,” the team member said.

Former New York Mayor Rudolph W. Giuliani is officially open to being attorney general in a Trump administration, and New Jersey Gov. Chris Christie, who might have trouble surviving confirmation to a Cabinet post, is being suggested as a natural chief of staff.

Mr. Giuliani and Mr. Christie, both top Trump surrogates during the campaign, are two of many names surfacing as potential picks for top government posts in the next administration.

“I certainly have the energy, and there’s probably nobody that knows the Justice Department better than me,” Mr. Giuliani, an associate attorney general in the Reagan administration, said Thursday on CNN.

Mr. Christie, who is running Mr. Trump’s transition team, could also be attorney general or homeland security secretary — though after the recent convictions of top aides in the Bridgegate scandal, a confirmation hearing might be touchy. Chief of staff would offer him a top post without having to face a Senate vote.

“The bottom line is that I have a job to do to help get the administration ready,” Mr. Christie said Thursday on NBC’s “Today” program. “If there’s some role for me that I want to do and that the president-elect wants me to do, we’ve known each other for 14 years — we’ll talk about it.”

Another name that has been mentioned for a possible chief of staff role is Republican National Committee Chairman Reince Priebus, who helped Mr. Trump win a stunning victory over Hillary Clinton and oversaw the party’s successful efforts to keep its majorities in the U.S. House and Senate.

Mr. Priebus said on Fox News on Thursday that he wasn’t sure if he saw himself having a role in the administration and such decisions would be up to Mr. Trump.

Steve Bannon, Mr. Trump’s campaign CEO, was also reportedly under consideration for the chief of staff post.

The list of potential Cabinet members is populated with members of Congress who work on those areas.

Rep. Jeff Miller, Florida Republican, is said to be a leading candidate for secretary to clean up the Department of Veterans Affairs. As chairman of the House Veterans’ Affairs Committee, he is a chief critic of the way the Obama administration has run the VA.

Oklahoma Gov. Mary Fallin and former Alaska Gov. Sarah Palin are mooted to be on the list to head the Interior Department.

The Wall Street Journal reported Thursday that Rep. Jeb Hensarling, the Texas Republican who chairs the House Financial Services Committee, is being considered for Treasury secretary.

Other loyal supporters who could be in line for a Cabinet or secretary position are Sen. Jeff Sessions of Alabama, former House Speaker Newt Gingrich and retired neurosurgeon Ben Carson.

Mr. Gingrich told radio host Sean Hannity this week that he could envision himself as sort of a “senior planner” — “trying to think through how we fundamentally, at the most basic levels, restructure the federal government.”

A few people said to be on Mr. Trump’s short list for key national security posts are House Homeland Security Committee Chairman Rep. Michael T. McCaul, Texas Republican, and retired Lt. Gen. Michael T. Flynn, the former director of the Defense Intelligence Agency.

Sources say Mr. Trump is closely considering Mr. Flynn to be national security adviser, while Mr. McCaul is being eyed for the Homeland Security Department’s top job.

Keith Kellogg, a retired Army lieutenant general, is in charge of the transition on the defense side, which also includes the Department of Veterans Affairs, and Mira Ricardel, who was acting assistant secretary of defense in the George W. Bush administration, is working under Mr. Kellogg, Defense One reported this week.

Kansas Secretary of State Kris Kobach, a staunch illegal immigration opponent and early Trump supporter, told The Wichita Eagle this week that he has been asked to join Mr. Trump’s transition team but said he had no expectation of an offer for an administration post.

Mr. Carson, another former rival of Mr. Trump’s who was a top surrogate, would seemingly fit the job description for secretary of the Department of Health and Human Services.

“These are all things that are under discussion,” Mr. Carson said Thursday on Fox News. “I think you can do a lot from outside the government, myself.”

State Department deputy spokesman Mark Toner said the Trump camp had not sent an envoy to begin discussing the transition process.

While the defeat of Mrs. Clinton, a former secretary of state, has been a source of much hand-wringing behind the scenes at the department, career diplomats have indicated that they will be ready to work with the Trump administration.

Mr. Toner said as much Wednesday, telling reporters that “when you choose a path of public service, you do so with the recognition that … you have to compartmentalize your own political beliefs from your professional duties.”

“That is something that is incumbent on any public servant, whether it’s at the State Department or any other federal agency, or the military for that matter,” he said. “That’s what, frankly, provides continuity and institutional knowledge for our government. So I wouldn’t predict any mass exodus, far from it.”

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