Mr. Kushner allegedly proposed establishing a secure, secret communications channel between the Trump transition team and the Kremlin during a December 2016 meeting with Mr. Kislyak in New York City, the Post reported.
"No", McMaster said. "We have back-channel communications with a number of countries".
Lt. Gen. H.R. McMaster, the national security adviser, declined to say whether he would be concerned if a private citizen attempted to set up backchannel communications with a foreign government to influence U.S. foreign policy and said he would not be concerned if a White House official attempted to do so.
The Post reported that the direct line between the transition team and the Kremlin in concept would have been conducted through Russian diplomatic facilities to avoid being monitored in American communication systems.
Also, Reuters has reported that Mr Kushner had at least three previously undisclosed contacts with Mr Kislyak during and after the 2016 campaign.
Trump's chief economic adviser Gary Cohn declined to answer questions about Kushner, telling Politico, "We're not going to comment on Jared".
In the days after the meeting with Kislyak, Kushner had a separate meeting with Sergey Gorkov, a Russian banker with close ties to Russian President Vladimir Putin.
This month, the Justice Department named Robert Mueller, a former Federal Bureau of Investigation director, as an independent special counsel in the probe, setting off alarms at the White House and stoking fears that it will have to endure a protracted investigation that may involve extended interviews with current officials.
Kushner was a trusted Trump adviser a year ago, overseeing the campaign's digital strategy, and remains an influential confidant within the White House as does his wife, Ivanka Trump. And less than two weeks later, the idea was dropped, said the report.
Reports that the FBI has now turned its attention to Kushner-though he is reportedly not the formal subject of a probe or the target of a criminal investigation-mean the investigation has reached the White House, increasing pressure on the Trump administration.
A source close to Kushner said Kushner was unaware of the FBI's interest in him and hasn't been contacted.
Federal investigators and several congressional committees are looking into Russia-Trump campaign connections.
The Post reported earlier that investigators are focusing on meetings he held in December with Moscow's ambassador and the head of a Russian bank that has been under United States sanctions since 2014.
"Mr. Kushner previously volunteered to share with Congress what he knows about these meetings", Gorelick said in a statement Thursday.
The committee also has asked Trump's campaign to produce all documents, emails and telephone records going back to the beginning of his run for the White House in June 2015, the Washington Post also reported on Friday, citing two unnamed people who were briefed on the request. "If it's been publicly reported that he met with Russians, and the investigation has to do with administration officials meeting with Russians, well, then, they'll probably want to talk to everybody".
The controversy has spilled beyond the political circles of Washington, with USA stock markets selling off strongly when Trump's Russian Federation revelations were first reported. The White House did not acknowledge any other contacts between Kushner and Russian officials. A White House official has confirmed plans for supporters meetings.
The Russian intelligence at issue purported to show that former Attorney General Lynch had been compromised in the Clinton investigation.
At the time, Mr Kushner was a private citizen, but working in Mr Trump's transition team.