Trump has been mulling removing Nielsen, a Kelly protege who became the secretary at Homeland Security when he left the job to become Trump's chief of staff, for a number of weeks, the source said.
The source cautioned Trump could still change his mind on the matter, but said he has grown weary of her in his push to harden the U.S. border with Mexico.
Trump has not decided on a candidate to replace Nielsen, the Wall Street Journal reported.
"The Secretary is honored to lead the men and women of DHS and is committed to implementing the President's security-focused agenda to protect Americans from all threats and will continue to do so," said Tyler Houlton, a Department of Homeland Security spokesman, in response to an ABC News report about the possible staff changes.
Trump is also considering replacing Kelly, an ardent defender of Nielsen, with Vice President Mike Pence's chief of staff, Nick Ayers, the source said.
Kelly, a retired Marine Corps general, has sought to bring more stability to the White House operation under the unpredictable Trump.
During his time as chief of staff, he and the president have had a rocky relationship, according to various news reports and Bob Woodward's best-selling book "Fear: Trump in the White House."
If they leave, Kelly and Nielsen would join a long list of people who have been fired by Trump or resigned since he took office in January, 2017. That list includes former Secretary of State Rex Tillerson and former Attorney General Jeff Sessions, who was removed by the president last week. (Reporting by Steve Holland, Tim Ahmann and Makini Brice; Editing by Jeffrey Benkoe and Alistair Bell)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)