The whistleblower's lawyer, Andrew Bakaj, told the Times that "any decision to report any perceived identifying information of the whistle-blower is deeply concerning and reckless, as it can place the individual in harm's way."

The complaint and a memorandum of that call were both made public this week.

That information about the whistleblower, who raised alarms about Trump's July 25 call with Ukraine President Volodymyr Zelensky, was first reported by The New York Times on Thursday.

The whistleblower who accused President Donald Trump of pressuring Ukraine's president to interfere in the 2020 presidential election is a CIA employee who was detailed to the White House, NBC News reported Friday.

"The whistleblower has a right to anonymity," Bakaj said.

Bakaj did not provide a comment to CNBC.

Mark Zaid, another lawyer for the whistleblower, told NBC News: "Publishing details about the whistleblower will only lead to identification of someone, whether our client or the wrong person, as the whistleblower. This will place this individual in a much more dangerous situation, not only in their professional world but also their possible personal safety."

In the complaint, which was made public Thursday by the House Intelligence Committee, the whistleblower said that more than half a dozen U.S. officials told him about the details of that phone call "in the course of my official duties."

But little else is currently known to the public about the whistleblower, whom Democratic lawmakers have said should be called to testify before Congress. Lawyers for the whistleblower have signaled that their client is willing to testify.

The whistleblower accused Trump in the call of "using the power of his office to solicit interference from a foreign country in the 2020 U.S. election" by asking Zelensky to investigate allegations of wrongdoing against former Vice President Joe Biden and his son Hunter.

Neither the White House nor a lawyer for the whistleblower responded to CNBC's request for comment on reports with information about the whistleblower. The CIA did not immediately respond to CNBC's request for comment.

Reporting about the complaint sparked a firestorm on Capitol Hill, leading dozens of Democratic lawmakers to come out in support of an impeachment inquiry into Trump. House Speaker Nancy Pelosi, who had long resisted pressure from her caucus to pursue impeaching Trump, announced a formal impeachment inquiry on Tuesday.