Specifically, he questioned his role in the firings of Michael Flynn and James Comey, sources told Vanity Fair.
Former Trump campaign aide Sam Nunberg told the publication Mr Kushner was the "worst political adviser in the White House in modern history", claiming: "I’m only saying publicly what everyone says behind the scenes at Fox News, in conservative media, and the Senate and Congress."
It comes just days after Mr Mueller issued indictments for two of Mr Trump's former campaign staffers, reportedly causing mass panic among Mr Trump's inner circle.
"The walls are closing in," one senior Republican close to the White House told the New York Post. "Everyone is freaking out."
The indictments included charges against Mr Trump's former campaign manager, Paul Manafort, and former adviser George Papadopoulos.
Mr Nunberg said: "Here’s what Manafort’s indictment tells me: Mueller is going to go over every financial dealing of Jared Kushner and the Trump Organization.
Mr Trump continued to dismiss the indictments as “fake news” after their release, and attempted to shift the focus to Hillary Clinton’s dealings with Russia.
However, a majority of voters said in a recent opinion poll they did not believe the Russia story was fake, and supported Mr Mueller's investigation into the Trump campaign.
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