The Times states that Rosenstein discussed secretly recording Trump and using the 25th Amendment to remove him from office with officials at the Department of Justice and the Federal Bureau of Investigation.
The President's reliance on his memo caught Rosenstein by surprise, and he became angry at Trump, according to people who spoke to Rosenstein at the time.
"The New York Times's story is inaccurate and factually incorrect", he said.
Because of Rosenstein's crucial role in overseeing the Russian Federation probe, there was immediate speculation that the memos may have been leaked in order to damage Rosenstein, and by extension Mueller - more than to hurt Trump.
None of his proposals appear to have been acted upon, according to the Times, but the report will nearly certainly increase Trump's ire at the deputy attorney general - and potentially put his job in jeopardy. Rosenstein was also reportedly displeased by the way Trump tried to replace Comey.
The extreme suggestions show Mr. Rosenstein's state of mind in the disorienting days that followed Mr. Comey's dismissal.
Members of the president's cabinet are required to notify Congress they do not believe a president can carry out his or her duties, with powers removed if both houses back their assessment by a two-thirds vote.
Mr Rosenstein has been a frequent punching bag for Trump supporters for appointing Special Counsel Robert Mueller in May 2017 to take over a federal probe of suspected Russian meddling in the USA election and potential coordination between Moscow and the Trump campaign.
(The scoop indicates that the identity of the person who wrote the anonymous op-ed is "unknown" to the paper's news side.) Now Trump & Co. will have either a pretext or solid grounds - depending on where you stand on matters of governance or partisan politics - to launch fresh attacks against Rosenstein, not to mention Mueller. The White House initially held up that memo as justification for Comey's firing, though Trump himself has said he was thinking about "this Russian Federation thing" when he made the move. The report also noted that Rosenstein discussed recruiting cabinet members to remove Trump from office by invoking the 25th Amendment.
"But let me be clear about this: Based on my personal dealings with the president, there is no basis to invoke the 25th Amendment", Rosenstein said.
This official and a source who was in the room characterized Rosenstein's remark as sarcastic. One participant asked whether Mr. Rosenstein was serious, and he replied animatedly that he was. "I would never suggest this, but I will tell you, oy, they're so lucky that we're peaceful". Beyond the speculation about Rosenstein, it was revealed that Trump's former fixer, Michael Cohen, is cooperating with special counsel Robert Mueller's investigation.
He chose Mueller for the job one week after he laid the groundwork for the firing of Comey by writing a memo that criticized Comey's handling of the FBI's investigation of Clinton's email server. Rosenstein appointed Mueller that May. Perhaps worse, however, is how misleadingly the Times presented the story, creating a narrative that doesn't necessarily match up with what the sources said. "Today", tweeted Ingraham, who added in another tweet that the deputy attorney general "must be fired today", tagging Trump's Twitter account.