(CNN) Now that President Donald Trump's former "fixer," Michael Cohen, has been sentenced to prison, leaders of the House and Senate Intelligence committees are preparing to haul him back before Congress before he begins serving time.

He's not the only one.

The Senate Intelligence Committee is also seeking to speak to other officials in Trump's orbit who have been charged in special counsel Robert Mueller's investigation, including former national security adviser Michael Flynn, former Trump campaign chairman Paul Manafort, his former deputy Rick Gates and former campaign adviser George Papadopoulos, according to committee leaders and sources familiar with the probe.

"I think it's safe to say if they were indicted, they were on our list," Senate Intelligence Chairman Richard Burr, a North Carolina Republican, told CNN. "We potentially will talk to a lot of folks."

The witnesses, if they testify, would help the Senate Intelligence Committee fill in key blanks in its investigation into 2016 Russian election interference, which has remained a bipartisan probe as it's stretched on for nearly two years, though it has yet to reach consensus on whether the Trump campaign conspired with the Kremlin. Burr and Sen. Mark Warner of Virginia, the panel's top Democrat, have waited to speak to -- or in some cases re-interview -- several key officials after they agreed to cooperate with Mueller, but the opportunity could soon be approaching.

The committee has been engaged in discussions with the special counsel and defense attorneys to get access to several cooperating Mueller witnesses in addition to Cohen, including Flynn, Papadopoulos and Gates, according to a source familiar with the investigation.

The panel has also continued to revisit past interviews as it has learned more, including from Mueller's court filings, another source familiar with the probe said.

"There were a number of witnesses that they needed to go through the legal proceedings with Mueller first," Warner said. "Once those proceedings are finished" the committee can move forward, he said, "and for many of them they are finished now."

The expected incoming chairman of the House Intelligence Committee, Democratic Rep. Adam Schiff of California, has also expressed a desire to speak again to Cohen, who testified behind closed doors before both intelligence panels last year. Schiff has said he's in touch with Cohen's legal team, too.

Schiff told CNN he also wants to interview Trump's longtime friend Roger Stone, as well as Stone's confidant Jerome Corsi, about their contacts with WikiLeaks. But those two men are fighting the special counsel, and it's unclear whether Congress will succeed in bringing them in to testify.

"We certainly are going to want to continue the investigative lead thread about ... the contacts Trump campaign associates had with WikiLeaks," Schiff said, adding that Stone's 2017 testimony before his panel "may have been far less than truthful."

Cohen willing to testify

Cohen was sentenced Wednesday to three years in prison on a number of charges, including lying to Congress about the proposed Trump Tower Moscow project when he testified last year.

He was scheduled to report to prison by March 6. Cohen's lawyer Lanny Davis said in a statement that his client was willing to speak to Congress again once Mueller's investigation is complete. "At the appropriate time, after Mr. Mueller completes his investigation and issues his final report, I look forward to assisting Michael to state publicly all he knows about Mr. Trump -- and that includes any appropriate congressional committee interested in the search for truth and the difference between facts and lies," Davis said.

But it's not clear whether congressional leaders will wait for Mueller, since the special counsel has not tipped his hand to when he will wrap up.

"I'm not sure how we get him from jail," Burr said Wednesday. "I can only tell you we're in conversations and have been with Michael Cohen's legal staff, and we think there's a great likelihood he will come in to talk to us."

Asked if he would issue a subpoena for Cohen's testimony, Burr said: "We'll chat."

It's unclear what Burr knows about details from Mueller's filing that a Russian national approached Cohen in 2015 offering "political synergy" with the Trump campaign. Asked about the revelation, Burr said: "I think it all dealt with business. He was doing a business deal."

Negotiating with other witnesses

The Senate committee has also been engaged with others who were sentenced in the Mueller probe.

The panel sought testimony from Papadopoulos, for instance, but he requested immunity from the committee before he was interviewed, CNN reported in October. Papadopoulos has since served his two-week sentence for lying to the FBI.

The committee reached out to Flynn in the opening days of its Russia probe, although he had requested immunity in March 2017 to testify. The committee has continued to stay in touch with Flynn's attorneys as he's pleaded guilty and subsequently cooperated with Mueller, one of the sources said. Flynn will be sentenced later this month, and the special counsel has recommended no jail time.

The committee interviewed Manafort last year before he was indicted by the special counsel -- and before many twists and turns tied to the Russia investigations were unearthed -- although pursuing another interview with him could be more complicated, given that the special counsel is now accusing Manafort of lying after he had agreed to cooperate.

Jason Maloni, a spokesman for Manafort, said that if the committee sends Manafort a formal request to appear, he would address it.

"Mr. Manafort answered every question he was asked, and I've never heard concerns raised that he was anything other than honest and forthright," Maloni said of Manafort's July 2017 testimony.

Warner said there was no way to know yet what the special counsel probe may have uncovered that the Senate investigation hasn't learned, though he acknowledged Mueller had more tools to convince witnesses to talk.

"There are a number of key individuals who, because of the power to bring criminal charges, they clearly have been more cooperative with Mueller," Warner said. "He has more leverage over some of the key witnesses, and in many cases, you know, we get to a certain point and then we run into someone who is under the Mueller investigation."

Burr said at a forum last month that the Senate Intelligence Committee has referred multiple individuals to the special counsel for prosecution, including for lying to the committee, a charge that Cohen pleaded guilty to last week.

Schiff has suggested that witnesses may have lied during his committee's Russia investigation, too, such as Stone, though Stone has denied he lied. Schiff says he wants to send his panel's interview transcripts to Mueller if they aren't released publicly before Democrats take control of the House next month.

"It's our intention to make them available ASAP to the special counsel," Schiff said.

On Wednesday, Warner said he was eager to learn exactly what it was that Cohen had lied to the committee about -- and what else he had told Mueller.

"I'm anxious to learn what those are," Warner said. "What other stories, what other facts did Mr. Cohen lay out to the special prosecutor?"