Speaking on CBS News on Sunday, reporter Steven Portney said that the now former DHS head will be "forever" remembered for her policy of child separation.
Senior administration officials told CNN that Nielsen had a 5 p.m. meeting at the White House with Trump where she was planning to discuss with him the immigration and border issues and a path forward.
She has served as DHS secretary since December 2017, and she has fiercely defended many controversial immigration policies.
Trump and Nielsen have battled behind the scenes over the administration's immigration policy and efforts to build a wall on the southern border.
The announcement she is leaving her post comes the day after the president visited the southern border.
".I am pleased to announce that Kevin McAleenan, the current U.S. Customs and Border Protection Commissioner, will become Acting Secretary for [DHS] I have confidence that Kevin will do a great job!"
Last June, protesters booed Ms Nielsen as she ate at a Mexican restaurant in Washington DC. And during the government shutdown over Trump's insistence for funding for a border wall, Nielsen's stock inside the White House even appeared to rise.
Trump insists that the arrival of immigrants across the southern USA border constitutes a national emergency so important that he sidestepped Congress' refusal to provide him with several billion dollars he requested to build the border wall.
Her relationship with Mr Trump is said to have been hard, although in public she has been unwaveringly loyal to the administration.
Nielsen was tapped to lead the agency after Gen. John Kelly left to take up the chief of staff position in the White House. Noting that the department now has neither a permanent secretary nor deputy secretary, he called on the administration to work with Congress in good faith to keep the country safe. She had no intention of resigning, according to one of the sources, but rather was going there with an agenda. Fox News has not confirmed the report.