Washington (CNN) Prosecutors told a federal judge on Sunday they are nearly ready to unseal details from court proceedings about how President Donald Trump's former campaign chairman Paul Manafort lied during his cooperation, including about efforts to sway the President's approach to Ukraine.

Unsealing the details could potentially explain major questions about Manafort's connections to the White House and fill in gaps about what Russia and Ukraine hoped from Trump after he took office.

Early last year, Judge Amy Berman Jackson determined Manafort "intentionally" lied to then-special counsel Robert Mueller and a grand jury about multiple topics during his cooperation after he pleaded guilty in late 2018 about: $125,000 he received for the legal bills, about another unnamed Justice Department criminal investigation, and about his interactions with his longtime Russian associate Konstantin Kilimnik while he was Trump's campaign chairman and later.

Prosecutors said Manafort lied about 2017 and 2018 discussions with Kilimnik about Ukrainian policy, specifically, a Ukraine "peace plan" that would provide a "backdoor" way for Russia to control part of Ukraine, and their interest in getting Trump's support for it, according to the Mueller report. The FBI believes Kilimnik has ties to Russian intelligence, according to court filings and the Mueller report.

Heavily redacted documents

Jackson held multiple lengthy court hearings about the topics as Mueller's prosecutors sought to unravel Manafort's cooperation deal and have him sentenced. While the judge released versions of those transcripts before his sentencing in March 2019, they were heavily redacted, leaving out many details regarding what prosecutors had learned and what Manafort told them.

The details have stayed heavily redacted while Mueller wrapped up his investigation and related criminal cases wound down. The Washington Post sued for access to the details last March, around the time Manafort was sentenced to seven years in prison for financial and Ukraine lobbying-related crimes.

"Having conferred with counsel for Manafort and reviewed the records at issue, the government believes that some of the redactions are no longer necessary," prosecutors wrote on Sunday.

That doesn't mean the details will be made public immediately, however. Prosecutors and Manafort's team told the judge in their filing they'd like to review the redacted sections again before they're public, and other parts of the Justice Department may be consulted too.

Manafort's team and the DC US Attorney's Office have asked for at least two more months before the judge lifts the redactions on the documents, according to the filing.

Jackson has not yet responded to the update on Sunday.

Questions surrounding Ukraine

It's unclear if and how the Kilimnik-Manafort peace plan episode might relate to Trump's more recent tangles with Ukraine , which involved his Mueller-investigation personal attorney Rudy Giuliani's dealings there and led to his impeachment by the House of Representatives.

At very least, Manafort's discussions about Trump and Ukraine and the Giuliani efforts both show the interest Eastern European powers had taken in gaining Trump's attention.

Mueller, in his final report, had made clear Manafort and Kilimnik discussed swaying Trump on Ukraine.

"After the presidential election, Kilimnik wrote an email to Manafort expressing the view—which Manafort later said he shared—that the plan's success would require U.S. support to succeed: 'all that is required to start the process is a very minor 'wink' (or slight push) from [Donald Trump],'" the Mueller report says. "The email also stated that if Manafort were designated as the U.S. representative and started the process, [former Ukrainian President Viktor] Yanukovych would ensure his reception in Russia 'at the very top level.'"

Mueller had also asked Trump directly about the supposed Ukraine policy. The President responded in writing that he did not remember hearing from Manafort about any policies Russia or Ukraine sought.

"The Office has not uncovered evidence that Manafort brought the Ukraine peace plan to the attention of the Trump Campaign or the Trump Administration. Kilimnik continued his efforts to promote the peace plan to the Executive Branch (e.g., U.S. Department of State) into the summer of 2018," Mueller wrote in his final report on Russian interference in the election.

Mueller also noted that he could not access all of Manafort's electronic communications and that Manafort had lied to investigators.