The new chairman of the House Intelligence Committee, Rep. Adam Schiff Adam Bennett SchiffOvernight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings Democrats, advocates seethe over Florida voting rights ruling MORE (D-Calif.), suggested this week that senior White House adviser Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE and President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE's former chief strategist Stephen Bannon invoked “bogus privileges” to avoid answering certain questions in their testimonies before lawmakers as part of the committee's Russia probe.

During an interview that aired on Friday on Hill.TV's "Rising," Schiff said his committee hopes to bring back a number of witnesses, including Trump's former personal attorney Michael Cohen Michael Dean CohenMichael Cohen: Trump taxes would reveal 'wealth is not as significant' as he says Michael Cohen: Trump's dislike of Obama is 'purely racial' Michael Cohen blames 'Stockholm syndrome' for letting Trump leer at his daughter MORE, as part of its investigation into Russian election interference, which was brought to a close last year by Republicans who at the time controlled the intel panel.

“There were any number of witnesses, and he was one of them, who would simply refuse to answer questions they didn’t want to answer because they felt it might incriminate them or might incriminate others or they simply had their own reasons they wouldn’t share with the committee,” Schiff said. “Sometimes they claimed bogus privileges, in the case of Jared Kushner or Don Jr. or Steve Bannon Stephen (Steve) Kevin BannonJuan Williams: Swamp creature at the White House Engineers say privately funded border wall is poorly constructed and set to fail: report Bannon and Maxwell cases display DOJ press strategy chutzpah MORE there were claims of attorney client privilege or the White House asked me not to."

The White House did not immediately respond to a request for comment.

Schiff said that there are a number of witnesses who the committee is interested in bringing back for more testimony as part of the Russia investigation, and Kushner might be one of them.

“He may be one of those people. He did come and testify before the committee there were a number of questions he was not willing to answer,” Schiff said, adding that he would “love” to invite Cohen back.

In November, Cohen pleaded guilty to lying to Congress about the timing of plans relating to efforts to build a Trump Tower in Moscow. He also agreed to cooperate with special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE's own Russia investigation, according to a plea deal released by the special counsel.

Schiff said one of the committee’s early steps would be to provide Mueller with transcripts from their witnesses to compare notes and see “whether witnesses have been truthful before Congress.”

House Speaker Nancy Pelosi Nancy PelosiPowell warns failure to reach COVID-19 deal could 'scar and damage' economy Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) announced Thursday that she has selected Schiff to lead the House Intelligence Committee. Democratic House committee chairs are prepared to launch multiple investigations into Trump.

—Tess Bonn