Jan. 6 panel moving closer to Trump's inner circle -- with Rudy Giuliani and Ivanka in their sights: report

The House select committee hopes the recent testimony by Donald Trump's son-in-law and former senior adviser Jared Kushner will prompt others in the president's inner circle to cooperate with their investigation.

The panel has conducted more than 800 depositions and interviews and has more than 100 remaining on its schedule, including one with a key witness whose testimony on Tuesday is expected to link the Oath Keepers and Proud Boys militia groups to the Jan. 6 insurrection, sources told The Guardian.

That deposition could help the committee establish whether Trump oversaw a criminal conspiracy as he attempted to undo his 2020 election loss, and that crucial evidence could potentially link the White House to "Stop the Steal" rally organizers and the militia groups that stormed the U.S. Capitol.

The committee also hopes to resolve efforts to talk to former Trump attorney Rudy Giuliani and Ivanka Trump now that Kushner has spoken to investigators, according to The Guardian, which cited "sources familiar with the matter."

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The panel is especially interested in speaking to Giuliani, who oversaw the scheme to pressure Mike Pence to stop the certification of Joe Biden's election win, but investigators still have been unable to reach an agreement with him on the parameters of their discussion, including matters of executive privilege.

Investigators hope that Trump's daughter, who seems to have understood before Jan. 6 the scheme was unlawful, can help them establish whether the former president was aware that stopping the certification was unlawful but pursued the plan anyway.

The select committee has not yet decided whether to compel cooperation from Ginni Thomas, the wife of Supreme Court justice Clarence Thomas, about her text messages to former White House chief of staff Mark Meadows about overturning the election results.

Several committee members were not aware of Thomas's texts, which had been turned over by Meadows months ago, until they were reported late last month, but members who knew about them had already decided that calling her to testify would turn the inquiry into a political circus.