Just this morning, in a puzzlingly phrased missive, Trump bemoaned reports that he is under investigation for obstruction of justice after abruptly firing FBI Director James Comey last month. Comey said he believes Trump ultimately fired him "because of the Russian Federation investigation".
The president, for his part, has denied any collusion between members of his campaign and Russian agents looking to interfere with the election.
In a tweet earlier Friday, Trump said nobody has been able to show any proof about his collusion with Moscow after months of investigations.
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. Trump also acknowledged, for the first time publicly, that he is under federal investigation.
On Thursday, Trump took aim at the report special counsel Robert Mueller is investigating the president for obstruction of justice. "I can go around them".
Days after Comey was abruptly ousted, Rosenstein appointed Robert Mueller as special counsel to investigate Russian involvement in the 2016 presidential election and possible collusion with the Trump campaign.
The investigation appears to be reaching a broadening circle of current and former officials.
Terming Comey's allegations untrue, Trump later said he was willing to testify under oath but Mueller's reported investigation into the president's actions means that Trump will have to live with the ghost of another probe reaching to the White House.
The Washington Post, citing five people who spoke on condition of anonymity, said Mr Dan Coats, the director of national intelligence, Mr Mike Rogers, the head of the National Security Agency, and Mr Richard Ledgett, the former deputy director at the NSA, had agreed to be interviewed by Mr Mueller's investigators as early as this week.
Meanwhile, members of Trump's transition team were ordered to preserve documents and other material related to the Russian Federation investigation, the New York Times reported.
Significantly, Preet Bharara, the India-born former top U.S. federal prosecutor, earlier this week had said that there was enough evidence to begin an obstruction of justice case against Trump over his alleged interference in the Russian Federation probe.