Rep. Adam Kinzinger, a Republican from Illinois, is seen last fall.
CNN  — 

House Speaker Nancy Pelosi is weighing new ways to help beef up the bipartisan credibility of an investigation into the deadly Capitol riots — an issue that has taken on renewed importance after the GOP walked out on the January 6 select committee.

With extra seats on the panel, Pelosi is now seriously considering naming GOP Rep. Adam Kinzinger of Illinois to the committee, multiple sources tell CNN, with one House Democrat with knowledge saying there has been “much discussion about Kinzinger” and “it could happen today or tomorrow.”

And the speaker is also looking to potentially hire a Republican as an outside adviser or staffer for the committee, sources tell CNN. Former Rep. Denver Riggleman, a Virginia Republican and former intelligence officer who has been an outspoken critic of former President Donald Trump, was seen heading into the speaker’s office for a meeting Thursday afternoon.

During a news conference on Capitol Hill on Thursday morning, Pelosi said, “We’ll see,” when asked about potentially appointing a Republican to the panel.

“I mean, there are some members that would like to be on it,” Pelosi added. “But, we’ll see.”

Rep. Bennie Thompson, the chairman of the select committee, said adding Kinzinger “has been discussed” with Pelosi – and said adding the Illinois Republican would be a “welcome addition.”

“I think the speaker’s leadership on appointing people who actually want to get to the facts, and not giving people who have already determined that President Biden was at fault – that’s completely out of the realm of reality,” Thompson, a Mississippi Democrat, told CNN. “We will follow the facts.”

Kinzinger, a vocal Republican critic of Trump who was one of 10 House Republicans to vote for his second impeachment, would join Rep. Liz Cheney of Wyoming as the only Republicans on the new select committee. House Minority Leader Kevin McCarthy pulled his five GOP members from the panel, after Pelosi rejected two of McCarthy’s five choices – Reps. Jim Banks of Indiana and Jim Jordan of Ohio — for their roles in pushing to overturn the presidential election results.

Kinzinger refused to comment about his potential appointment to the panel on Thursday morning.

While Democrats are completely comfortable with Pelosi’s decision to veto McCarthy’s picks, they are still cognizant that the GOP will try to use the move as fresh ammo in their attacks on the probe. But the potential new Republican additions to the committee — along with Cheney’s high-profile presence on the panel — may bring more legitimacy to one of the most consequential investigations ever conducted by Congress and make it harder for Republicans to argue that it’s a partisan endeavor.

Emerging from a planning session in Pelosi’s office on Thursday, which included fellow members on the select committee, Cheney said that Kinzinger would be a “tremendous addition” to the panel. She added that she’d be supportive of the move, but noted it’s ultimately up to the speaker.

Cheney, who has been vocal about the need for a sober and serious investigation, has also been pushing behind the scenes for Pelosi to hire a Republican as an outside adviser or staffer, sources tell CNN. The Wyoming Republican met with Riggleman earlier Thursday, ahead of his Pelosi meeting.

The committee is scheduled to hold its first hearing next week, which will feature testimony from police officers who defended the Capitol on January 6. Logistical details of the hearing are still coming together, but investigators want to play videos of the deadly attack and body-worn camera footage from some of the police officers, according to a source familiar with the planning, in an effort to paint a vivid, first-hand account of the assault that day.

When asked what she hopes to get out of the first hearing, Cheney called it an opportunity to hear first-hand from the “brave” officers who put their lives on the line, “put some facts on the table,” and “counter some of the attempts at whitewash.”

If Kinzinger is asked to join the committee and he accepts, the Illinois Republican is sure to face blowback from his own party — something Cheney has experienced in spades.

Cheney was already booted from GOP leadership earlier this year, but Republicans are once again agitating for her to be punished now that she’s back in the spotlight. Republicans could kick her off the House Armed Services Committee or expel her from the entire GOP conference, though the latter would require two-thirds support from House Republicans.

Still, there appears to be little appetite among top Republicans to go that route, worried it could serve as distraction as they seek to rally around a unified midterm message.

“We have a lot of other issues that we’ve got to deal with,” said Rep. Drew Ferguson of Georgia, a member of GOP leadership. “We ain’t worried about what color to paint the fire hydrant.”

This story and headline have been updated with additional developments Thursday.

CNN’s Annie Grayer and Lauren Fox contributed to this report.