Politico first reported Trump had chosen Nielsen.
The White House said Nielsen has "extensive professional experience in the areas of homeland security policy and strategy, cybersecurity, critical infrastructure and emergency management".
The official announcement could come as soon as Wednesday, although the officials cautioned nothing is set until Trump publicly announces her as the pick.
The White House will nominate Kirstjen Nielsen to head the Department of Homeland Security, a senior US government official confirmed to FedScoop.
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Nielsen is considered an expert on cyber security, one of the primary issues under the Homeland Security Department's sprawling portfolio.
Kirstjen Nielsen, left, will be nominated to replace her former boss, John Kelly, as Secretary of Homeland Security. People close to her "have counseled her to lighten up and to pay more attention to the perfunctory niceties of a not-so-nice-job", they wrote when she became deputy White House chief of staff.
Duke was criticized in September when she described Hurricane Maria relief efforts in Puerto Rico - where a large majority of the population still lacks electricity - as a "good news story". Increased border security and a possible overhaul of the immigration system remain top campaign promises Trump has yet to fulfill, including his trademark wall on the border with Mexico.
She also worked for the Transportation and Security Administration under former President George W. Bush. She was responsible for carrying out some of Kelly's orders on who gets access to the president.