Asked about Rosenstein's departure, first reported by ABC News, White House spokeswoman Sarah Sanders said she had not spoken to Rosenstein and would leave any announced departures to him or the president.
According to ABC News, Rosenstein had planned to serve as deputy attorney general for around two years, and he will stay on through Barr's confirmation to assure a smooth transition.
If confirmed, Barr, who was U.S. Attorney General under the late President George H.W. Bush from 1991 to 1993, would oversee the investigation led by U.S. Special Counsel Robert Mueller, a fellow Republican chosen by Rosenstein. Senate Minority Leader Chuck Schumer called on Mr. Trump to rescind Barr's nomination Wednesday, claiming that Barr would not be able to objectively oversee the Mueller investigation.
Soon after, Rosenstein named Mueller as special counsel.
Rosenstein reportedly made the decision on his own, and is not being forced out of his position by the White House. Barr would most likely take over that role, since Rosenstein only assumed it after former Attorney General Jeff Sessions recused himself.
In September the New York Times reported, citing anonymous sources, that Mr Rosenstein had discussed recruiting cabinet members to invoke the 25th amendment of the United States constitution, which provides for the removal of a president if he is deemed unfit for office.
"So the deep concern will be if he comes in and Rosenstein is gone, is this just a preface to either undercutting the investigation or trying to keep the results of it hidden from the American public".
Attorney General nominee William Barr (left) is meeting with senators including Judiciary Committee member Sen.
Mueller is investigating potential conspiracy between Trump's 2016 campaign and Russian Federation as well as whether the president has unlawfully sought to obstruct the probe.
Mr Rosenstein has yet to comment on the reports.
"Much of the bad blood with Russia is caused by the Fake & Corrupt Russia Investigation, headed up by the all Democrat loyalists, or people that worked for Obama", the President tweeted in April. He also said that Barr's memo was "his opinion of the slippery slope of obstruction of justice charges against a president who wants to terminate a political appointee". He said Barr would be an "excellent attorney general when he is confirmed".