"Very organised process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!" Trump said in a tweet.
Trump's tweet came as media reported that differences have come up within his camp on finalising his Cabinet.
A week after Trump, 70, was elected in a historic election, the President-elect is yet to name a member of his Cabinet.
The CNN reported that Trump's son-in-law and close adviser Jared Kushner is at the center of the "infighting" inside his transition team.
Trump has already replaced New Jersey Governor Chris Christie with Vice-President-elect Mike Pence as head of the transition team.
Christie was New Jersey attorney general when Kushner's father was tried and jailed in the state for tax evasion, illegal campaign contributions and witness tampering in 2004.
The Wall Street Journal reported the Vice President-elect Mike Pence yesterday ordered removal of all lobbyists from the transition team.
Rogers said 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 on 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 Christie, who previously headed up the transition team's efforts until being replaced by Pence.
Pence yesterday provided to the White House the necessary paper work that would facilitate smooth transition.
Trump slammed The New York Times for writing "incorrect
and misleading stories" about his transition team.
"The failing @nytimes story is so totally wrong on transition. It is going so smoothly. Also, I have spoken to many foreign leaders," Trump said in a tweet.
In another tweet Trump said he has received and taken calls from many foreign leaders after his victory in the November 8 presidential election.
"Australia, New Zealand, and more. I am always available to them. @nytimes is just upset that they looked like fools in their coverage of me," he continued.
Trump also denied reports about getting top security clearance for his children.
"I am not trying to get top level security clearance for my children...This was a typically false news story," Trump said.
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