(CNN) The House intelligence committee plans to interview Susan Rice next month as part of its investigation into Russia meddling in the US election last year, a high-profile target for Republicans who accuse President Barack Obama's former national security adviser of improperly handling classified intelligence reports, according to sources familiar with the private talks.

President Donald Trump and Republicans have focused on allegations that Rice revealed the names of Trump's transition aides in intelligence reports -- called "unmasking" -- saying that Obama officials were seeking to divulge damaging information about the Trump campaign.

Rice has vehemently denied doing anything wrong . But she has yet to answer questions from lawmakers, including declining a request to appear before a Senate judiciary subcommittee in May. And now, she has agreed to appear in a closed-door session that is expected to take place before the House departs for its August recess.

"Ambassador Rice is cooperating with bipartisan Russia investigations conducted by the Intelligence Committees as she said she would," said Erin Pelton, a spokesperson for Rice, who served as national security adviser and the US ambassador to the United Nations under Obama.

The move comes as both the House and Senate inquiries begin to take shape, with high-profile witnesses expected to appear behind closed doors before lawmakers depart for their August recess. On the Senate side, top Democratic member Mark Warner told CNN Thursday that the panel may need more records from former Trump campaign chairman Paul Manafort and his former national security adviser, Michael Flynn , as the inquiry ramps up.

"I think we're still going through that," Warner said of the Flynn and Manafort records the panel received so far. "I think we may need more information."

And he added that the Senate panel is now sifting through "two batches" of documents from the Treasury Department to assess whether there are any financial links between Trump associates and Russian officials.

"We're just starting that review," Warner said.

North Carolina Sen. Richard Burr, the chairman of the Senate committee, would not say when the high-profile Trump witnesses would come before his panel, including the President's son-in-law, Jared Kushner.

But Kushner's security clearance forms -- and whether he properly disclosed his contacts with foreign officials -- have become a ripe target for the Senate judiciary committee, which is asking the White House and FBI for more information about Kushner's records.

"One needs to know what was the reason the security form was not addressed correctly," Sen. Dianne Feinstein, ranking member on the Senate Judiciary Committee, told CNN Thursday. "I'm not going to say what the reasons are, we need to know what his reason is for making that error because it's a substantial error."

Moreover, Senate Judiciary Chairman Chuck Grassley, R-Iowa, and Sen. Lindsey Graham, R-South Carolina, have called on the FBI to provide more information about whether there were warrants issued under the Foreign Intelligence Surveillance Act for former Trump associates during the campaign season as part of the FBI investigation into Russian meddling and possible coordination with Trump officials.

"As to FISA warrants, I want to know was there ever a warrant issued against anybody in the Trump world?" Graham told CNN Thursday. "Was there probably cause found by a judge that would allow a warrant to be issued, and if that person was surveilled, did anything come of it?"

On the House side, Rep. Devin Nunes, chairman of the House intelligence committee, issued three subpoenas last month for information about unmasking by former Obama administration officials, including Rice. It's unclear if Nunes -- who stepped aside from leading the Russia probe amid controversy -- will participate in the interview of Rice.

Two weeks after Nunes took a secret trip to the White House grounds to review intelligence about unmasking, Bloomberg reported that Rice had "unmasked" the names of Trump transition aides in classified reports. Three days after Rice's name was revealed, Nunes became the subject of a House ethics probe into whether he revealed classified information and was forced to step aside from leading the House Russia investigation.

In April, CNN reported, according to multiple sources in both parties , that Republican and Democratic lawmakers who reviewed the intelligence reports found no evidence that Obama administration officials did anything unusual or illegal.

Texas Rep. Mike Conaway , who is now leading the Russia investigation, declined to comment Thursday on Rice's appearance.

Rice has denied doing anything wrong, telling MSNBC in April, "The allegation is that somehow the Obama administration officials utilized intelligence for political purposes. That's absolutely false."

Rice declined an invitation from Graham, who is helping lead the Senate judiciary committee's Russia investigation, through her lawyer, because the top Democrat on that probe, Sen. Sheldon Whitehouse, opposed the invite.

At the time, Trump took to Twitter to take aim at Rice.

"Susan Rice, the former National Security Advisor to President Obama, is refusing to testify before a Senate Subcommittee next week on allegations of unmasking Trump transition officials. Not good!" Trump tweeted in May.

Republicans and Democrats on the House Russia probe have been inviting witnesses largely aligned with their partisan stances in the investigation. Republicans invited former Obama Pentagon official Evelyn Farkas earlier this week because they believe she leaked classified information about the federal investigation of the Trump campaign. Former Clinton campaign chairman John Podesta also testified this week to discuss how his emails were hacked and then released by Wikileaks in the final month of the 2016 election.