The Associated Press has learned that Kushner spoke with the Russian ambassador to the U.S. - Sergey Kislyak - about creating the secret line to make it easier to hold sensitive discussions about the conflict in Syria.
Kislyak allegedly told his higher-ups that Kushner floated the proposal for back-channel communications during a conversation between the two and former National Security Advisor Mike Flynn at Trump Tower on December 1 or December 2.
The FBI and the oversight committee - as well as several other congressional panels - are looking into Russian meddling in the 2016 presidential election.
The request suggests that the Senate committee is plowing ahead with its investigation, which focuses in part on possible collusion between the Trump campaign and Russian operatives, despite the appointment of a special counsel to oversee the sprawling federal Russia probe. Kushner's attorney, Jamie Gorelick, told Reuters that Kushner "has no recollection of the calls as described".
The White House referred calls to Kushner's attorney.
Obama officials told Washington Post reporters that the best they can surmise is perhaps Trump's campaign was afraid it'd get out to the media that they were trying to talk to the Russians.
A source connected to the data analytics group said the team has not been contacted about any Russian Federation related probe.
Kushner suggested using Russian diplomatic facilities in the United States for the communications and the proposal took Kislyak by surprise, the report said on Friday.
Also, Reuters has reported that Mr Kushner had at least three previously undisclosed contacts with Mr Kislyak during and after the 2016 campaign.
The White House declined to comment.
The Post reported last week that the Russian Federation investigation had been extended to a top White House official as a "significant person of interest".
The daily alleged that the discussion of a secret channel adds to a broader pattern of efforts by Trump's closest advisers to obscure their contacts with Russian counterparts.
A former U.S. ambassador to North Atlantic Treaty Organisation who has served in both Bush administrations and under President Clinton issued a strong rebuke Friday night of President Trump's relationship with Russian Federation.
The sources stress that the talk between Kushner and the Russian envoy about communications was focused on the US response to the crisis in Syria and other policy-related matters.
Another potential line of inquiry could concern Kushner's failure to disclose some of his contacts with Russian government officials when he was filling out his application for a security clearance.
Trump has repeatedly denied any collusion between his campaign and the Kremlin, amid accusations from USA intelligence that Russian President Vladimir Putin orchestrated a sweeping campaign to tilt the vote in the Republican's favor. The president defended the intelligence sharing and said he had "the absolute right" to share information about ISIS plots involving airplanes with the two top Russian diplomats.