California Democratic Rep. Adam Schiff disclosed in an interview Sunday that Democrats are in talks with counsel for former Trump attorney Michael Cohen to "bring him back" for further testimony, less than two weeks after Cohen pleaded guilty to lying to Congress in 2017 about an abandoned Trump Tower project in Moscow.

Schiff suggested Cohen will return voluntarily. If Schiff becomes the chairman of the House Intelligence Committee when Democrats retake the House in January, as expected, he would have the power to subpoena Cohen to testify and provide documents -- but Cohen would retain the option of pleading his Fifth Amendment right to avoid self-incrimination.

"We're already in touch with his counsel; we hope to bring him back," Schiff told CBS News' "Face the Nation" host Margaret Brennan.

Cohen admitted in his surprise guilty plea late last month that he falsely told the Senate Intelligence Committee that work on the project stopped in January 2016, when in fact efforts continued until further on in the presidential campaign season: June 2016. That case was brought by Special Counsel Robert Mueller.

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"We're already in touch with his counsel; we hope to bring him back." — Rep. Adam Schiff, D-Calif.

Schiff, who has faced President Trump's ire in part over his dogged pursuit of Russia-related matters in the past two years, said Cohen could provide insight on whether Trump or his associates told Cohen to lie about the Moscow project.

"He can shed not only light on this -- but one of the most intriguing bits of the sentencing memo was the Special Counsel's representation that Michael Cohen has evidence concerning officials at the Trump organization," Schiff said, referring to the sentencing memo filed Friday by Mueller's team.

"The core issue in Muller's investigation, that core issue, is collusion or conspiracy," Schiff continued. "And so, who are those Trump Organization officials, are they family members of the president? What is the evidence they have? It looks like this is separate and apart from the evidence on the Trump Tower Moscow deal."

Cohen said he lied in order to stay consistent with the Trump team's political messaging at the time, which was that the then-candidate had limited connections with Russia.

"It's clear from the filing that Michael Cohen, in the preparation of his false testimony to Congress, circulated that among people affiliated with the administration or White House," Schiff said. "That may go to the obstruction-of-justice issue."

Schiff also suggested Cohen could provide information on potential campaign-finance violations by the president. Cohen separately pleaded guilty in August to several charges brought by prosecutors in the Southern District of New York (SDNY), including five counts of tax evasion, one count of making false statements to a financial institution, one count of willfully causing an unlawful corporate contribution and one count of making an excessive campaign contribution.

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As part of his guilty plea in the SDNY case, Cohen said he had arranged hush-money payments to adult-film star Stormy Daniels and former Playboy model Karen McDougal “in coordination with and at the direction” of then-candidate Trump.

SDNY prosecutors have called for Cohen to receive "a substantial term of imprisonment despite his cooperation" when he is set to be sentenced in that case by a New York judge on Wednesday.

Mueller, meanwhile, has asked the court to give "due consideration" to Cohen's cooperation when sentencing him for the separate charge of lying to Congress, and any sentence Cohen receives in the Mueller prosecution will likely run concurrently with his punishment in the SDNY case.

For his part, Trump has called Cohen a corrupt and unfaithful liar who should receive a "full and complete" sentence.

Legal experts were split on the significance of the plea for Trump, because prosecutors would have to show not only that the hush money payment constituted a "campaign contribution" that would not have been made if not for the campaign, but also that Trump knew he was breaking the law.

Although candidates like Trump legally can contribute whatever they want to their campaigns, they must disclose their contributions. Intermediaries such as Cohen are bound by strict spending limits.

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Campaign-finance violations typically are treated as civil -- rather than criminal -- matters. In 2013, the Federal Election Commission issued a $400,000 fine against Barack Obama's 2008 presidential campaign over a slew of administrative campaign-finance violations.

Schiff, acknowledging that standing Justice Department guidelines precluded the indictment of a sitting president, suggested that Trump might not get off so easy.

The Democrat insisted the "Justice Department doesn't think there's any problem of proving that this was intended to principally affect the election" and that the hush money payments therefore constituted campaign contributions that needed to be reported publicly.

"My takeaway is there's a very real prospect that on the day Donald Trump leaves office, the Justice Department may indict him," Schiff told Brenann. "He may be the first president in quite some time to face the real prospect of jail time."