The recommendation by Defense Secretary Ash Carter and Director of National Intelligence James Clapper was made last month, according to The Washington Post
, which first reported the recommendation.
The replacement of such a senior person would be unprecedented at a time when the US intelligence community has repeatedly warned about the threat of cyberattacks.
A major reason for their recommendation is the belief that Rogers was not working fast enough on a critical reorganization to address the cyberthreat. The Obama administration has wanted to keep the NSA dealing with signals intelligence, which would be a civilian-led agency, and a separate cybercommand which would remain under the military, the official told CNN.
Right now, one man, Rogers, heads both. He took over as head of the NSA and Cyber Command in April 2014.
The official said the initial plan was to announce the reorganization and that given the shift of personnel, Rogers would be thanked for his service and then move on.
Another issue -- but not the sole driving factor in removing Rogers, according to the source -- is a continuing concern about security.
Harold Martin, a former contractor for Booz Allen who was working at the NSA, has been charged and is being held without bail after allegedly stealing a large amount of classified information. Prosecutors allege he stole the names of "numerous" covert US agents. He was arrested in August after federal authorities uncovered what they have described as mountains of highly classified intelligence in his car, home and shed, which they said had been accumulated over many years.
Martin's motivation remains unclear, and federal authorities have not alleged that he gave or sold the information to anyone.
Potential role in Trump administration
Separately, this comes as Rogers is one of those under consideration by President-elect Donald Trump to be the next director of national intelligence, CNN has previously reported. Rogers went on a private trip on Thursday to meet with Trump, a trip that took many administration officials by surprise.
Some officials also have complained about Rogers' leadership style, according to the Post.
The Pentagon declined to comment, as did a spokesman for the director of national intelligence. The NSA did not return a request for comment.
The idea for dividing NSA's efforts has been in the works for a while.
"So we had them both in the same location and able to work with one another. That has worked very well, but it's not necessarily going to -- the right approach to those missions overall in the long run. And we need to look at that and it's not just a matter of NSA and CYBERCOM," Carter told a tech industry group in September.