The Washington Post reported Friday that Kislyak told his superiors that he and Kushner discussed setting up a secret communications channel between the Trump transition team and the Kremlin. After that Kislyak set up a meeting with Sergey Gorkov, the head of the Russian-owned VEB Bank.
The White House has not responded to CBS News' requests for comment.
Points of focus that pertain to Kushner include: the Trump campaign's 2016 data analytics operation; his relationship with former national security adviser Michael Flynn; and Kushner's own contacts with Russians, according to USA officials briefed on the probe.
The newspaper says Ambassador Sergei Kislyak told his superiors that Kushner proposed using Russian diplomatic facilities for their discussions, apparently to make them more hard to monitor.More news: Brewers keep it close but give up 4-2 loss
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The Russian intelligence at issue purported to show that then-Attorney General Lynch had been compromised in the Clinton investigation.
Jared Kushner, a senior adviser to Trump, will be involved in the new strategic messaging operation, as will Steve Bannon, another top adviser who specializes in managing Trump's populist appeal and shaping his political image, the sources said.
Kushner, a key White House adviser, had meetings late past year with Russia's ambassador to the U.S., Sergey Kislyak, and Russian banker Sergey Gorkov. Kislyak was said to be "taken aback" by the idea that "an American would use Russian communications gear at its embassy or consulate", the Post reported.
Kusher's attorney Jamie Gorelick said his client "has no recollection of the calls as described". The omissions were described as an "administrative error" by Gorelick, who said additional information about his meetings were provided to the Federal Bureau of Investigation the day after he submitted his incomplete clearance application.
"I called for his clearance to be suspended last month".
Also in attendance at that meeting was Mr. Trump's pick to be national security adviser, Michael Flynn, who was later fired for misleading the vice president about the nature of his conversations with Kislyak.
"Given his position and his contacts, interviewing him would be an important step in any thorough investigation", Hinnen said.