The discussions also included speculation about which Cabinet members could be on board with the idea, McCabe said in an interview with CBS's Scott Pelley. Rosenstein, through a Justice Department spokesperson, has repeatedly disputed McCabe's characterization of his remarks, though he has not denied the topic was discussed at some point.
The comments resurface the extraordinary tension between Trump and the nation's top law enforcement officials, though a number of the ones who worked with McCabe in the early days of the administration have since been dismissed or resigned.
Rosenstein "raised the issue (of the 25th Amendment) and discussed it with me in the context of thinking about how many other Cabinet officials might support such an effort," McCabe said in a transcript released by CBS on Friday.
He added that Rosenstein was "counting votes or possible votes" of different Cabinet members who he thought would support removing the President. When Pelley asked if Rosenstein seemed focused on getting rid of Trump, McCabe said he couldn't confirm that but Rosenstein "was definitely very concerned about the President, about his capacity and about his intent at that point in time."
Rosenstein's discussion of the 25th Amendment was "just another kinda topic that he jumped to in the midst ... of a wide-ranging conversation," McCabe added.
Earlier Friday, a spokeswoman for McCabe disputed characterizations of the incident.
"To clarify, at no time did Mr. McCabe participate in any extended discussions about the use of the 25th Amendment, nor is he aware of such discussions," Melissa Schwartz said in a statement.
She said McCabe was "present and participated in a discussion that included a comment by Deputy Attorney General (Rod) Rosenstein regarding the 25th Amendment."
It was not mentioned in the material released from the McCabe interview if he or anyone else approached Cabinet members directly to discuss the idea.
In a statement on Thursday, a Justice Department spokesperson said Rosenstein -- who repeatedly disputed the "wire" revelation back in September -- again denied pursuing or advocating for the use of the 25th Amendment to remove Trump from office.
"As the Deputy Attorney General previously has stated, based on his personal dealings with the President, there is no basis to invoke the 25th Amendment, nor was the DAG in a position to consider invoking the 25th Amendment," the statement read.
Both Trump and the White House on Thursday called McCabe a "disgrace," with the White House saying he had "no credibility" and Trump accusing him of being politically biased during his time at the FBI.
Vice President Mike Pence told MSNBC's Andrea Mitchell on Thursday he has "never heard any discussion of the 25th Amendment by members of this government and I would never expect to." Senate Judiciary Chairman Lindsey Graham called McCabe's comments "a stunning revelation" and that he would subpoena the former official to testify on Capitol Hill about the matter "if I have to."
McCabe said that the day after Comey's firing and after meeting with Trump in the Oval Office, "I met with the team investigating the Russia cases and I asked the team to go back and conduct an assessment to determine where are we with these efforts and what steps do we need to take going forward."
"I was very concerned that I was able to put the Russia case on absolutely solid ground in an indelible fashion that, were I removed quickly or reassigned or fired, that the case could not be closed or vanish in the night without a trace," said McCabe, who is promoting his forthcoming book, "The Threat: How the FBI Protects America in the Age of Terror and Trump."
In its statement on Thursday, the White House called McCabe's investigation "completely baseless."
CLARIFICATION: This story has been updated to more accurately characterize a statement from a Justice Department spokesperson.
CNN's Caroline Kelly, Manu Raju and Veronica Stracqualursi contributed to this report.