The Washington Post and NBC News reported Thursday that the FBI had turned its attention on Kushner's meetings as part of its larger investigation into Russian election meddling and possible collusion between the Trump campaign and Russia.
But White House staff have noted, according to a New York Times report, that in his occasional dressings-down of his staff Trump has lately included Kushner, whereas at the beginning of his campaign and his administration Kushner was usually immune.
That follows a recent report from The Washington Post alleging that Kushner wanted to develop a secure, private line with Russian Federation.
Corker said it appears to him that Kushner is "not a target, so I think I would just wait". In March the White House disclosed that the two had met, but the Post's sources say that the Federal Bureau of Investigation has taken an interest in what was discussed.
Rep. Adam Schiff of California said the government needed to "get to the bottom" of the matter and urged a review of Kushner's security clearance "to find out whether he was truthful".
The spotlight on Kushner grew brighter following a report in The Washington Post on Friday stating he talked about establishing a secure and secret communication channel between the Kremlin and the Trump transition with Russian Ambassador Sergey Kislyak during a meeting in December.
In a familiar refrain, Trump tweeted that it was "fake news", but he is now under considerable pressure, with several investigations under way into his team's links with Russian Federation, which is accused of hacking Democratic Party emails in order to help Trump win the White House.More news: Trump withdrawal from climate deal gets mixed response from US companies
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National Security Adviser H.R. McMaster told reporters in an off-camera news conference that he does not find backchannel communications with Russian Federation problematic.
"Back channels like this are the regular course of business, and that's really all that we know", Conway said.
"It is my opinion that numerous leaks coming out of the White House are fabricated lies", he tweeted.
He said that Kushner's contacts with the Russians, if true, present "a real problem" in whether President Trump's son-in-law should be trusted.
It is unclear who first proposed the communications channel, but the people familiar with the meeting said the idea was to have Mr. Flynn speak directly with a senior military official in Moscow to discuss Syria and other security issues.
The Post spoke with "people familiar with the matter", "officials", "current and former USA intelligence officials" and other unnamed sources in reporting the story.