Jared Kushner, one of President Donald Trump's top advisers, faces a Nov. 27 deadline to hand over emails to a Senate committee investigating alleged Russian interference in the 2016 presidential election.
Republican Sen. Chuck Grassley of Iowa, the chair of the Senate Judiciary Committee, and ranking Democrat Sen. Dianne Feinstein of California addressed a letter to Kushner's attorney stating that Trump's son-in-law had failed to provide emails relevant to the inquiry, the New York Daily News reported.
The emails requested by Grassley and Feinstein relate to hacktivist site WikiLeaks, an alleged Russian attempt to set up back channel communications with the Trump campaign, and exchanges with Michael Flynn, who was fired as Trump's national security adviser in February 2017.
The Judiciary Committee has said it will subpoena the files if Kushner fails to hand them over.
Kushner has cooperated with the Senate investigation to date. He maintains that members of the Trump campaign did not collaborate with Russia.
Abbe Lowell, Kushner's attorney, described Kushner as a "hero" because he instructed campaign staffers not to have dealings with foreign nationals.
Special counsel Robert Mueller is leading his own investigation into Russian involvement. Members of Mueller's team are expected to interview senior Trump administration officials in the coming weeks, including the top lawyer at the White House, Don McGahn.
"The White House counsel would be in the position to know about the decisions that relate to the investigation," Neil Eggleston, who served as White House counsel during the Obama administration, told CNN. The top White House lawyer "would be the person who interfaces with the Justice Department and the person the president would most likely talk to about those issues."
Before his position at the White House, McGahn was the chief attorney for the Trump presidential campaign.
The CNN report speculated that McGahn could seek to withhold information from the inquiry, either by invoking attorney-client privilege or by having Trump assert executive privilege.
However, White House special counsel Ty Cobb dismissed such suggestions.
"I have no reason to believe McGahn won't fully cooperate," Cobb added.
"We want the special counsel to be able to say he got everything he asked for, so the American people can trust what he decides," said Cobb.
Mueller's inquiry has already overcome one instance where a lawyer sought to avoid testifying by asserting attorney-client privilege. Melissa Laurenza, a lawyer for Paul Manafort and Rick Gates, initially sought to avoid testifying by invoking attorney-client privilege.
However, a federal judge compelled her to answer questions after he ruled that Manafort and Gates had involved Laurenza in the foreign agents registration-related offense they are accused of committing.