One person close to Nielsen said she is miserable in her job.
According to the New York Times' report, Trump has been angry that Nielsen has been "resisting his direction that parents be separated from their children when families cross illegally into the United States".
Trump was furious with Nielsen, telling her he didn't think she was doing enough to secure the border.
The White House declined specific comment on whether Trump berated Nielsen, her assumed resignation letter and on whether Trump maintained confidence in Nielsen, who shot at DHS in December. Another report from Politico noted that Trump is growing increasingly frustrated with Nielsen, and the knives may be coming out for her.
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Nielsen reportedly told colleagues that she was close to resigning after the incident and had already drafted a resignation letter, the Times said, citing "several current and former officials familiar with the episode".
Trump, she told the Times, is "rightly frustrated that existing loopholes and the lack of congressional action have prevented this administration from fully securing the border".
The secretary added, "Border security is the most basic and necessary responsibility of a sovereign nation". At the meeting, both Nielsen and Attorney General Jeff Sessions tried in vain to explain to Donald Trump that the federal government can not completely shut down the border. They spoke on condition of anonymity because they were not authorized to disclose private conversations.
One person familiar with Trump's blowup at the meeting said it was prompted by a discussion about why Mexico was not doing more to prevent illegal border crossings into the United States. Trump went on a Twitter tear, writing that he'd told Nielsen to block the migrants from entering the U.S.
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White House press secretary Sarah Sanders was asked about the incident in Thursday's press briefing. He urged voters to "give me some reinforcements, please" in the form of new Republican members.
Trump has let his frustration surrounding immigration issues be known to the public, especially recently, as a caravan of about 150 migrants from Central America made its way to the southern border.
While border apprehensions dipped past year to their lowest levels ever, the numbers have been ticking up in recent months, returning to more typical historical levels.
The incident came amidst the president's frustration over his administration's failure to fully fund the border wall. A conviction for illegal entry carries a maximum penalty of six months in custody for first-time crossers, though they usually do far less time, and two years for repeat offenses.
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Hard-liners on immigration say Mr. Trump's anger is partly explained by a suspicion inside the West Wing that Ms. Nielsen, who served on the Homeland Security Council in the George W. Bush administration, is not sufficiently committed to Mr. Trump's agenda of tougher immigration policies.