The newspaper reported that Rosenstein, frustrated with the hiring process for a new Federal Bureau of Investigation director, offered to wear a "wire" and secretly record the president when he visited the White House.
None of Rosenstein's suggestions were implemented, as far as the sources speaking to the Times are aware. Schumer says other top administration officials remain in their jobs despite having had critical comments about Trump attributed to them.
Rosenstein's position has appeared to be in peril since past year, as Trump has leveled frequent attacks on him over the Russian Federation probe.
Deputy Attorney General Rod Rosenstein suggested a year ago that he secretly record President Trump to expose the turmoil in the White House - and said he also discussed asking cabinet members to invoke the 25th Amendment to remove the president from office. According to the Times, Rosenstein told four Justice Department officials, plus then-Acting FBI Director Andrew McCabe, that the president wasn't taking the process seriously.
If the president believes the piece in the New York Times--and the president is the severest critic of the New York Times in the country. He also said that "based on my personal dealings with the president, there is no basis to invoke the 25th Amendment".
Wallace said the story will raise questions about Rosenstein's frame of mind right around the time he appointed Special Counsel Robert Mueller to investigate potential collusion between the Trump campaign and Russian Federation.
Another official at the meeting, then-FBI lawyer Lisa Page, wrote her own memo of the discussion which does not mention any talk of the 25th amendment, according to a second person who was familiar with her account.
A source who was in the room told CNN that the wire comment was "sarcastic and was never discussed with any intention of recording a conversation with the President".
In conversations with allies, the report continues, the Deputy Attorney General vowed be would be "vindicated" for memo being pinned on him.
"Andrew McCabe drafted memos to memorialize significant discussions he had with high level officials and preserved them so he would have an accurate, contemporaneous record of those discussions".
The White House did not immediately comment on the Times story. Sitting in on Mr. Trump's interviews with prospective F.B.I. directors and facing attacks for his own role in Mr. Comey's firing, Mr. Rosenstein had an up-close view of the tumult.
"Shocked! Absolutely Shocked! Ohhh, who are we kidding at this point?"
Brooke Singman is a Politics Reporter for Fox News.