Rosenstein talked a year ago about invoking the 25th Amendment and wearing a wire during Trump meetings, the N.Y. Times' Adam Goldman and Michael S. Schmidt reported last week. Rosenstein denied the Times report as "inaccurate and factually incorrect".
Congressional Republicans, Democrats and some Trump aides have warned for months that the president shouldn't fire Rosenstein, saying such a move could lead to impeachment proceedings if the Democrats retake the House in the upcoming mid-terms.
Bloomberg reported the White House accepted Rosentein's resignation.
Rod Rosenstein, the United States deputy attorney general who oversees the Russian Federation investigation, is expected to leave his post on Monday after a bombshell news report that he discussed removing Donald Trump from office.
As it emerged that Mr Rosenstein was heading to the West Wing, it was variously reported that he had quit, was about to quit, or had been summoned to be fired - or for a dressing down.
"If Trump tries to shut down the investigation, he will provoke a constitutional crisis", Robenalt said.
That would have seen the president kicked out of the White House because of an unspecified "impairment" and Vice President Mike Pence take over his job.
Firing the deputy attorney general or forcing him to resign will also allow him to kill the redacted special counsel authorization - a document that likely contains "all the money-laundering, tax evasion, bank fraud, and conspiracy on which Manafort has been convicted", Sumner wrote.
But the president's attention was also divided while at Bedminster, as he was focused on developments in Brett Kavanaugh's Supreme Court confirmation hearings while also being urged by aides to prepare for the upcoming U.N. General Assembly.
"If the rumors of Deputy AG's Rosenstein's departure are true, I am deeply concerned that it puts that investigation at risk". In May, Rosenstein appointed special counsel Robert Mueller to look into Russian interference.
Other reports suggest that Rosenstein has resigned, or indeed, resigned before Trump had the chance to fire him.
On the flights both to and from a Missouri rally, Trump polled staff on the plane, called his outside network of advisers and kept a careful eye on what his favourite hosts on his favourite network were recommending.
McCabe memorialised discussions he had with Rosenstein and other senior officials in the stress-packed days immediately following James Comey's firing as Federal Bureau of Investigation director.
"He was hired by Jeff Sessions", Trump said in the interview, which was aired on "Fox & Friends".