The actions reportedly took place in the spring of 2017, shortly after Trump fired FBI Director James Comey, according to the New York Times.
A report indicates that Mr Rosenstein began discussions about removing Trump via the 25th amendment of the US constitution, which can be invoked if the President is incapable of fulfilling his duties.
He discussed this plan with top executive branch members, attempting to gain their support.
Sources told ABC News that he believed he could gain the support of Attorney General Jeff Sessions and then Homeland Security Secretary John Kelly.
In addition, he reportedly suggested secretly recording Trump to demonstrate that his administration is dysfunctional.
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A source confirmed that Mr Rosenstein had suggested making a recording, but claimed he did so sarcastically.
The 25th amendment can be invoked by the Vice-President with the support of a majority of top executive branch members or other bodies as defined by Congress.
If the amendment is invoked, power is passed to the Vice-President, who becomes acting President.
Mr Rosenstein responded sharply to the reports, releasing a statement strongly denying the allegations.
He said: “The New York Time’s story is inaccurate and factual incorrect.
“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.
“Based on my personal dealings with the President, there is no basis to invoke the 25th Amendment.”
Any attempt to remove Mr Rosenstein from his position would be highly controversial, as he is responsible for overseeing the Mueller inquiry into alleged Russian interference in the 2016 US presidential election, and whether there was any collusion with the Trump campaign.
Leading Democrat Congressman Chuck Schumer said that the report should not be used as a reason to fire Mr Rosenstein and replace him with “an official who will allow the President to interfere” in the Mueller inquiry.
President Trump strongly denies allegations of election collusion with Russia, and has described the investigation as a “witch hunt”.