The Times says Nielsen told colleagues after the meeting that "she should not continue in the job if the president did not view her as effective".
Ms. Nielsen, who is a protégée of John F. Kelly, the White House chief of staff, has drafted a resignation letter but has not submitted it, according to two of the people. It has been Nielsen's role to implement Trump's strict immigration policies at the borders, a job that has become hard as immigration advocates push back against the administration's tactics.
In late April, the president tasked Nielsen's Department of Homeland Security to contain and break up the traveling migrants.
Trump's outburst was not only aimed at Nielsen, according to the Times, but the entire cabinet for not making enough progress in stopping illegal immigration and ensuring border security.
Haberman's tweet came in response to a tweet by fellow New York Times reporter Julie Davis, who explained that Nielsen's resignation threat had been "a long time in coming" because "Nielsen and Trump have clashed often and she has been a frequent target of his freewheeling immigration rants".
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1 person in the assembly said Trump railed in the whole Cabinet on what he said was deficiency of advancement keeping out illegal immigrants, " the occasions said. "I share his frustration", Nielsen said, according to CNN.
When asked Thursday about the tense meeting, White House press secretary Sarah Sanders told ABC News, "The president is committed to fixing our broken immigration system and our porous borders".
"We are a country of laws and the president and his administration will enforce them". But Nielsen maintained her ground, citing the law in certain instances, the source said.
"All these are complicated matters and I will keep on to guide the Department to accomplish everything that we are able to in order to implement the President's security-focused schedule", she added, without saying anything regarding resignation programs.
Trump nominated Nielsen to lead the U.S. Department of Homeland Security.
As a group of Central American migrants seeking asylum in the USA approached the border in recent weeks, Trump directed Nielsen not to let the so-called "caravan" into the country.