The deputy attorney general has been managing special counsel Robert Mueller's Russian Federation investigation and has signaled to other officials that he would leave when he was satisfied that Mueller's investigation was either complete or close enough to completion that it was protected.
Rosenstein oversaw the Mueller investigation after former Attorney General Jeff Sessions recused himself from overseeing an investigation into a campaign in which he played an active part. Then-Attorney General Jeff Sessions, an early Trump supporter during the presidential campaign, had recused himself.
Rosenstein wants to ensure a smooth transition for incoming Attorney General nominee Bill Barr and plans to transition out of the job in the coming weeks, the sources said. He said Barr would be an "excellent attorney general when he is confirmed".
After the report broke, Trump promised to get rid of a "lingering stench" at the Justice Department, but weeks later stated that he had a "very good relationship" with Rosenstein, and had "no plans" to give the Deputy AG his marching orders.
Barr submitted a memo to the Justice Department past year that argued the law doesn't support an inquiry into whether Trump may have obstructed justice if he tried to frustrate the Russian Federation investigation.More news: Trump campaign chief gave polling data to Russian
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Whitaker also was critical or skeptical about the special counsel investigation. 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.
Meanwhile, Rosenstein has sparred with Republicans in Congress, especially former House Intelligence Committee Chairman Devin Nunes, R-Calif, over "slow walking" its response to document requests.
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.
Mr Rosenstein denied the report, which he said was "based on anonymous sources who are obviously biased against the department".
Trump nominated Rosenstein to the post in 2017.