During the meeting, Trump blamed Nielsen for what he said was her failure to secure USA borders, the newspaper cited the officials as saying.
White House press secretary Sarah Sanders was asked about the incident in Thursday's press briefing.
During the meeting, Trump yelled about the United States' porous border and said more needed to be done to fix it.
The White House declined specific comment on whether Trump berated Nielsen, her supposed resignation letter and on whether Trump retained confidence in Nielsen, who took over at DHS in December.
This has not been the first time Trump has berated his cabinet officials.
The secretary, he added, was "hard at work" Thursday "on the President's security-focused agenda and supporting the men and women of @DHSgov".
DHS oversees U.S. Customs and Border Protection.
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 exchange was so hostile, according to The New York Times, that Nielsen later informed colleagues that she planned to leave the administration and drafted a resignation letter, though she did not submit it.
Tyler Houlton, a spokesman for the Department of Homeland Security, disputed that Nielsen had drafted a resignation letter and was close to resigning, calling those assertions "false".
"I share his frustration", Nielsen's statement said. Nielsen issued her own statement Thursday evening saying the president is justifiably frustrated but that she is staying on the job. "We are a country of laws and the president and his administration will enforce them'".
Trump won the 2016 election largely on his promise to crack down on illegal immigration and build a wall that would totally shut down the flow of immigrants.
Immigrants from Honduras, Haiti, El Salvador and other countries who were given protected status to live in the United States should have a path to citizenship, White House Chief of Staff John Kelly told National Public Radio on Friday. He repeatedly claimed credit for the fact that during his first year in office, illegal border crossings dropped to their lowest levels in decades. "Border security is the most basic and necessary responsibility of a sovereign nation".
According to those familiar with the admonishment, Trump was unhappy with Nielsen's handling of border security; one source told the Times that the president went on a long tirade about Nielsen's lack of ability to tighten the U.S. -Mexico border and prevent undocumented immigrants from entering the country.
Nielsen reportedly pushed back at points, and argued that she was constrained by American immigration laws-a position Attorney General Jeff Sessions supported.