Rosenstein has stayed on under Acting Attorney General Matt Whitaker, whose controversial appointment has sparked numerous legal challenges and raised questions about what role he would play regarding the investigation.
When exactly Rosenstein leaves could shift depending on the timing of Barr's confirmation and the naming of a new deputy attorney general. Also, Rosenstein told senators during his 2017 confirmation hearing that he would not remain in his post if he believed that he was being pressured to influence any investigations.
Rosenstein's tentative plan to depart after Barr's confirmation was first reported by ABC News.
White House spokeswoman Sarah Huckabee Sanders told Fox News on Wednesday that Rosenstein had always planned to stick around two years.
The deputy attorney general reportedly made the decision to step down and was not forced out by the White House. Barr would most likely take over that role, since Rosenstein only assumed it after former Attorney General Jeff Sessions recused himself.
Barr met with Republican lawmakers as he works to build support for Senate confirmation as the top u.s. law enforcement official, and is slated to meet with the panel's top Democrat on Thursday, according to a department official.
Rosenstein was said to have discussed removing Trump from office or secretly recording conversations with him; he said he never authorized any action after those conversations but Justice Department sources said he expected to be fired.
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The person familiar with the plans said there was no specific date for Rosenstein's departure.
His former personal attorney, Michael Cohen, also pleaded guilty to a range of crime, including paying a pair of women alleging affairs with the President to keep quiet while Trump was running for office.
Trump has denounced the investigation as a witch hunt.
Rosenstein became a frequent target of Trump's ire on Twitter - with the president recently re-posting an image of him and other officials behind bars.
However Mr Rosenstein was stripped of the role late past year when Mr Sessions was forced out by the president.
He has accused the investigation of being led by "Democrat loyalists".