"Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!" he said.
Former Congressman Mike Rogers said Tuesday he parted ways with Trump's transition team, removing an establishment national security voice from the planning process of the next president's cabinet.
Rogers was told Monday on the phone that he was out, according to a source familiar with the transition. The source said this was part of an effort to replace the transition team members associated with New Jersey Governor Chris Christie, who previously headed up the transition team's efforts until being replaced by Vice President-elect Mike Pence.
"Sometimes in politics ... there are people who are in and people who are out. And the people who have been asked to move on have some relationship with Chris Christie," Rogers told CNN's Anderson Cooper Tuesday night.
"And so there's a whole series of about five of them that fit that criteria that were asked to leave in the last few days. And you know what? That's absolutely the campaign's prerogative. I hope they all stay engaged," he added.
Kushner has been rubbing allies the wrong way in his recent efforts to purge the transition team of Christie associates, sources say.
Kushner's father was prosecuted by then-US Attorney Christie in 2004 for tax evasion, witness tampering and illegal campaign contributions.
Rogers, who had been working on the transition team for months under Christie, was sidelined as the campaign and transitions merged into one presidential team, with members of Trump's inner circle that were with him through the campaign taking more prominent roles in the transition, according to one source familiar with the transition activity.
But another source, a longtime Christie associate, cautioned that there was no "purge" of Christie staff, the team that began the transition months ago, and that such a characterization is "overblown." While some Christie staff have left, others are continuing on with the transition team.
A high-ranking Trump insider said the so-called "purge" focused only on lobbyists.
The Christie associate said it makes sense that Pence would want some of his own people involved now that he is running the effort.
"I think there is some confusion going on about a chain of command coming out of New York. Hopefully they'll get that settled pretty soon. I think they're going to need to do it because as this clock ticks, all of these decisions become more important," Rogers told Cooper.
Earlier Tuesday, Rogers positively described his time period working with the transition team as a "privilege," in a statement to reporters, and said he was handing off his responsibilities as a national security adviser to the transition organization to Pence and "the stellar new leadership team."
"I look forward to continuing to provide advice and counsel as needed to the incoming Trump administration as they work to make America great again," Rogers said in the statement.
Speaking to CNN's Jim Sciutto on "The Lead," Rogers said later Tuesday that he felt the transition team was "going in a different direction," though he noted some confusion on the team.
"Is there a little confusion in New York? I think there is. I think this is growing pains," Rogers said.
The news of Rogers' departure was first reported by Bloomberg.
Rogers' participation in the transition team was seen as a heartening sign for traditional GOP national security advisers.
Sources tied to the transition team talking to CNN described the organization's internal disagreements -- mainly divided along the lines of establishment Republican operatives against more non-traditional influences on national security issues -- as a "knife fight" on Monday.
Rogers chaired the House Intelligence Committee while he was in Congress and is an Army veteran and former FBI agent with an expertise in national security
He has also been critical of Russia's role in recent hacking episodes, including the hacks of Democratic political groups during the election which the US government attributed to high levels of Russian government. Trump repeatedly declined to acknowledge Russia's role, saying the evidence was inconclusive.
Amid the churn in Trump's transition team the Obama White House Tuesday night said it's moving forward with a broader sharing of information.
"We received the MOU signed by Vice President-elect Pence this evening," said Brandi Hoffine, a White House spokesperson. "The next step is for the President-elect's transition team to provide us with the names of the individuals they have authorized to represent their transition effort across the government. Once we have received those names and related materials, those individuals will be able to receive the briefing materials we have prepared and begin to communicate with their Obama administration agency counterparts as we continue our work to facilitate the transition to the next administration."