The first charges stemming from special counsel Robert Mueller's investigation into Russian meddling in the 2016 election were reportedly filed on Friday, marking the most significant development yet in the inquiry that began a year ago.
United States media reports claim the target of the indictment could be arrested as soon as Monday.
Rosenstein appointed Mueller in May to lead the investigation into Russian meddling after FBI Director James Comey was sacked by President Trump.
Sources familiar with Mr Mueller's investigation said he has examined links between aides of Mr Trump and foreign governments, as well as possible money laundering, tax evasion and other financial crimes.
By June, Trump himself was reportedly under investigation for obstruction of justice.
President Trump had been repeatedly frustrated by the investigation since entering office, calling the probe a "witch hunt" and denying any collusion with Moscow.More news: Manchester United manager Jose Mourinho hails side's commitment after Spurs win
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A senior Trump official said Saturday that the White House will have "no comment" about the charges.
The allegation led to speculation that president might have obstructed justice by attempting to influence the Federal Bureau of Investigation probe.
US President Donald Trump shakes hands with Russia's President Vladimir Putin during their bilateral meeting at the G20 summit in Hamburg, Germany. He is also examining the possibility that the president may have tried to interfere with the Russian Federation investigation.
Mueller's team has also investigated Michael Flynn, who was an adviser to Trump's campaign and later briefly served as his national security adviser.
Flynn was sacked from the administration in February after it was found that he had misled vice president Mike Pence on his dealings with Russian officials.
It is unclear at this time what the charges are or who is facing them. Rosenstein oversees the Mueller probe at the Justice Department.