During a series of July 2017 meetings with fellow Justice Department and FBI officials, Rosenstein reportedly made the explosive suggestion of recording the president, and while the plot never materialized, he reportedly told then-FBI Deputy Director Andrew McCabe that he believed it was possible to convince Attorney General Jeff Sessions and then-Homeland Security Secretary John Kelly to later invoke the 25th Amendment.
"The New York Times story is inaccurate and factually incorrect", Rosenstein said in a statement. "I will not further comment on a story based on anonymous sources who are obviously biased against the department and are advancing their own personal agenda".
Mr. Rosenstein made these suggestions in the spring of 2017 when Mr. Trump's firing of James B. Comey as F.B.I. director plunged the White House into turmoil.
That person said the wire comment came in response to McCabe's own pushing for the Justice Department to open an investigation into the president.
After Rosenstein wrote a memo critical of Comey's handling of Democratic presidential candidate Hillary Clinton's email investigation, Trump used it as a basis for firing Comey.
Rosenstein denied the report in a statement to the Times.
The White House did not immediately respond to Fox News' request for comment on the report, but Trump's eldest son tweeted that "no one is shocked".
Rosenstein assumed oversight of the federal investigation into Russia's election interference previous year, after Sessions recused himself due to his own contacts with Russian officials during the campaign.
This would have been in the tumultuous days after James Comey was sacked as Federal Bureau of Investigation director, with the president citing in part a memo penned by Rosenstein.
The newspaper said its sources were people who were briefed either on the events themselves or on memos written by Federal Bureau of Investigation officials including Andrew McCabe, who became acting FBI director when Comey was sacked.
During the meeting, the Times says, Rosenstein raised the prospect of donning a "wire", prompting others in the room to inquire if the offer was genuine.
"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", McCabe's attorney Michael Bromwich said in a statement.