"I would give him the chance to see if he could do that because if there's nothing there, so you're not gonna find anything anyway", Carson said on Fox News Radio.
Comey said he believes Trump ultimately fired him "because of the Russian Federation investigation".
Kushner's attorney said such a review would be "standard practice".
"He's being investigated for taking the action that the attorney general and the deputy attorney general recommended him to take, by the agency that recommended he take the action. The president is not under investigation". "The president issued that tweet, that social media statement, based on a fake report, a report with no documented sources, from the Washington Post".
"The Department of Justice has a long-established policy to neither confirm nor deny such allegations".
Trump did not specify who he was referring to. But a department official said no one asked for the statement and Rosenstein acted on his own.
Trump Confirms Being Investigated for Firing Ex-FBI Director Comey
Jay Sekulow , a lawyer from US President Donald Trump's legal team, denied that Trump was under investigation. The White House initially claimed that Rosenstein's memo contributed to Trump's decision to fire Comey.
The five people spoke on the condition of anonymity because they were not authorized to discuss the matter publicly.
Rosenstein told a congressional panel this week that he was not in favour of firing Mueller without just cause.
The president has directed some of his frustration at Rosenstein and Mueller. Sen.
The accusations have been repeatedly dismissed as groundless by both the Kremlin and the Trump team. He repeated once again that he had never interfered in the FBI investigation and had not asked them to stop investigating his national security adviser Michael Flynn, who was suspected of having links with the Russian authorities.
Rosenstein, in office for less than two months, is the top Justice official overseeing the probe because Attorney General Jeff Sessions has recused himself.
Trump returned to the White House on Sunday after spending Father s Day weekend at the Camp David presidential retreat.
The president is not and has not been under investigation for obstruction, " lawyer Jay Sekulow from Trump's legal team told NBC's Meet The Press program.
Trump has fueled the concern in Congress by repeatedly calling the congressional and executive investigations into his campaign's ties with Russian Federation a "witch hunt".
A memorandum penned by Rosenstein was cited by the Trump White House as the inspiration for the May ouster of James Comey, then-director of the Federal Bureau of Investigation.
From 2011 until her confirmation, she was a lawyer for the U.S. Chamber of Commerce business lobbying group's legal arm, which played a major role in marshaling legal opposition to environmental and labor regulations championed by Democratic former President Barack Obama. The White House has not commented on this possibility.