Barr would most likely take over that role, since Rosenstein only assumed it after former Attorney General Jeff Sessions recused himself.
Rosenstein took charge of overseeing Mueller's Russian Federation probe after former Attorney General Jeff Sessions recused himself from the investigation.
"I know the deputy attorney general has always planned to roughly stay around two years", Sanders told "Fox & Friends" co-hosts. Lindsey Graham he would allow special counsel Robert Mueller's investigation to continue unabated, Graham said Wednesday.
Sources at the Justice Department say that although Rosenstein is expected to depart once Barr is in place, there isn't a specific plan or schedule in place that establishes dates or structure for that.
"I haven't spoken to the deputy attorney general myself, so I'll leave any announcements for him or the president to make when they want to do that, but certainly I don't think there's any willingness by the President or the White House to push him out", she noted.
Barr, Graham said, told him he didn't think Mueller was on a "witch hunt", as Trump has branded the Mueller probe.
Woman found dead in clothing donation bin
Police say she appears to have died after a medical episode, so the exact cause of death is not yet known. Canadian Press reported at the time that at least seven people had died in such bins in Canada since 2015.
William Barr, Trump's pick to replace Sessions who was sacked soon after the November midterm congressional elections, is set to appear for a confirmation hearing next week before the Senate Judiciary Committee, which must weigh his nomination before the full Senate considers his approval.
A person familiar with Rosenstein's thinking told HuffPost that there's now no concrete, specific plan in place for Rosenstein's resignation but said he's expecting to depart after Barr's confirmation.
Some Democrats expressed concern with Rosenstein's departure. Barr and Mueller worked together when Barr was Bush's attorney general between 1991 and 1993 and Mueller oversaw the department's criminal division.
After an embattled turn in that role, Sessions stepped down at the end of previous year and was replaced temporarily by Matthew Whitaker as Acting Attorney General.
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. Barr said he would go through the process of determining whether the Mueller report could be shared with Congress and the public when the report is finished, according to Graham.
Rosenstein has been frequently criticised by Trump, who calls the Russian Federation investigation a "witch-hunt" and denies any collusion with Moscow. Dianne Feinstein, D-Calif., the ranking member of the Judiciary Committee, when Barr's nomination was announced.