The interest in Kushner's activities by the special counsel's office is no more extensive than the FBI's interest in his multiple roles on both the Trump campaign and transition team, which CNN reported last month.
Kushner's attorney, Jamie Gorelick, told the Washington Post "we don't know what this report refers to".
Gorelick added, "Mr. Kushner previously volunteered to share with Congress what he knows about Russia-related matters".
Mueller's inquiry includes Kushner among other Trump's associates - former campaign chairman Paul Manafort and a campaign policy adviser Carter Page, The Washington Post claimed citing unnamed sources on Thursday.
Gorkov's state-owned bank Vnesheconombank (VEB) has been under USA sanctions since 2014.
CNN reported in March that Kushner met secretly with Russian ambassador Sergey Kislyak, the same official that Attorney General Jeff Sessions eventually acknowledged he met with at least two times during the presidential campaign.
Comey testified before the Senate last week, and stated that Trump spoke with him privately on several occasions in person and over the telephone.
An hour later, the president took to Twitter again, tweeting: "You are witnessing the single greatest WITCH HUNT in American political history - led by some very bad and conflicted people!" He continued to denounce ongoing congressional investigations into his campaign and Russian Federation, reiterated his disdain for the news media and touted what he perceived as his administration's successes. On Thursday, the Post reported that Vice President Mike Pence has retained outside counsel to help him weather whatever storm might come his way.
As Mueller assembles his investigative team, statements by Trump's friend Christopher Ruddy this week set off new questions.
The probe into Kushner's business dealings is part of the special counsel's investigation into Russia's interference in the 2016 presidential election.
Schlapp noted on "Outnumbered" that one of the attorneys, Jeannie Rhee, represented Hillary Clinton during the FBI investigation of her private email server.
"To the best of my recollection, I have never been directed to do anything I believe to be illegal, immoral, unethical or inappropriate", Rogers said at the hearing, without answering whether he was asked-but not directed-to back off.
According to the news accounts, neither Coats nor Rogers complied with Trump's requests. Coats told associates that Trump asked him whether he could intervene with Comey to get the Federal Bureau of Investigation to back off its focus on Flynn, the officials said.