The Washington Post was the first to report that Kushner wanted to set up a secret backchannel to communicate with Russian officials during the transition period between the election and Trump's inauguration.
American intelligence agencies first learned about the discussion several months ago, according to a senior American official who had been briefed on intelligence reports.
The discussion of a secret channel is the latest in a series of controversial reports and leaks regarding the Trump team's contacts with Russian Federation.
USA intelligence officials became aware of Kushner's suggestion to Kislyak for a secret channel after reviewing intercepts of the Russian ambassador's communications with Moscow following the meeting in New York City, according to the Washington Post.
The Post also reported that Mr. Kushner had proposed the communications channel and that it took Mr. Kislyak by surprise.
Two congressional committees and the FBI have launched investigations looking into, among other things, whether anyone in Mr Trump's team was aware of the Russian intervention.
And Oleg Deripaska, a Russian once close to Trump's former campaign manager, has offered to cooperate with congressional bodies probing alleged Russian meddling in the 2016 United States election, The New York Times reported Friday.
Current and former American officials said Mr. Kushner's activities, like those of many others around Mr. Trump, are under scrutiny as part of the investigation.
Trump's first national security adviser, Michael Flynn, also attended the meeting. Reuters reported at least two more previously undisclosed contacts - both phone calls between April and December. "He has no recollection of the calls as described", Jamie Gorelick said.
Setting up such a private channel between a foreign leader and a transition team would be unusual, according to the Post, though the State Department, the White House National Security Council, and the us intelligence agencies all have that ability.
The new information about the two calls as well as other details uncovered by Reuters shed light on when and why Kushner first attracted Federal Bureau of Investigation attention and show that his contacts with Russian envoy Sergei Kislyak were more extensive than the White House has acknowledged.
The Post previously reported that investigators are focusing on meetings he held in December with Kislyak and the head of a Russian bank that has been under U.S. sanctions since 2014.
Investigators believe Mr Kushner has significant information relevant to their inquiry, officials told NBC News.
As for Mr Kushner, he is apparently not looking to reduce his role as part of Mr Trump's team but he is said to have become increasingly tired of the scrutiny he has been placed under.
"We have backchannel communications with a number of countries", McMaster said in response to questions. Kushner initially failed to declare the meetings on forms to obtain a security clearance to serve in the White House.