The announcement on Thursday that Rosenstein will sit for a transcribed interview October 24 comes after weeks of negotiations over the meeting.
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Mueller is looking to release this new information sometime after the midterms.
On September 21, The New York Times reported that Rosenstein more recently suggested he secretly recorded the president a year ago to show the chaos of his administration.
Rosenstein vehemently denied the claim, and subsequent media reports also cast some doubt on the veracity of The Times' reporting.
Rosenstein went to the White House days after the report, expecting to be fired, but his job was spared, and he later flew with Trump on Air Force One to an global police chiefs' conference in Florida.
Trump also often gripes about Attorney General Jeff Sessions' decision to recuse himself from overseeing the investigation a year ago, after it emerged that he had not been forthcoming during his confirmation hearing about his contacts with Russians during the campaign.
"We don't need a special counsel". He echoed his calls for the deputy attorney general to resign in a series of tweets earlier in the day Thursday.
"He has not co-operated with Congress, failed to be transparent about his actions, and shown a lack of candour in the way he's characterized a number of events", Meadows tweeted.
"Special Counsel Robert Mueller is set to issue findings of some of the core aspects of his investigation into the alleged collusion between the Trump campaign and Russian Federation shortly after the November midterm elections", writes Fox News.
"It was interesting that yesterday, Rod Rosenstein has time to sit down with the Wall Street Journal, do a big, long interview, where he said the Mueller investigation is appropriate and moving in the right direction", Rep. Jim Jordan (R-OH) said Thursday, according to the Washington Examiner.