Prosecutors say Manafort's lies breached their plea agreement.
It remained unclear if the polling information Manafort allegedly shared was public or private, though it raises speculation that the data could have been used by the Russians to interfere in the election in an effort to support Trump's candidacy.
The accusation could be important evidence in Mueller's ongoing probe into potential coordination between the Trump campaign and the Kremlin.
Attorneys for Paul Manafort appeared to have mistakenly filed a court document Tuesday that made portions that were supposed to be redacted completely readable.
The Associated Press was able to review the material because it was not properly blacked out.
Mueller, who is investigating Russia's interference in the 2016 election, said in a court filing in March previous year that the Federal Bureau of Investigation assesses that Kilimnik "has ties to a Russian intelligence service and had such ties in 2016".
They contended the 69-year-old Manafort, facing years in prison, had breached the cooperation agreement that was reached when he pleaded guilty to cheating US tax authorities, violating federal lobbying laws and obstructing justice in connection with his long-time lobbying efforts for deposed Ukrainian leader Viktor Yanukovych in the years before he worked on Trump's campaign. They said he began talking with investigators before dawn, answering questions for "many hours" and "usually the entire day".
In the Tuesday filing, Manafort's lawyers said the disagreement can be dealt with through the sentencing process, because prosecutors have said they have no plans to file fresh charges.
In this photo from June 21, 2017, special counsel Robert Mueller departs after a meeting on Capitol Hill in Washington.
Kilimnik, who worked closely with Manafort, is believed to have close ties to Russian intelligence.
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Manafort sent Kilimnik, a former Russian military intelligence official, an email in April 2016, shortly after joining the campaign, suggesting that he sought to use his new position as leverage with Deripaska.
The latest allegations further detail how Manafort's work on the campaign intersected with his past global work with Kilimnik.
Manafort, 69, has already been convicted in one case brought by Mueller, and pleaded guilty in another, over financial crimes related to his work in Ukraine before the 2016 campaign, and for witness tampering, which also involved Kilimnik.
Through his spokesman, Manafort has acknowledged discussing the briefings but said they never occurred.
Another revelation that was meant to be kept under wraps was a meeting between Manafort and Mr. Kilimnik in Madrid.
Prosecutors have also accused Manafort of lying about his contacts with Trump administration officials, which defence lawyers also deny.
The proposal would involve Russia pulling forces from eastern Ukraine and allow Ukrainian voters decide whether Crimea should be leased to Russia 50 or 100 years, along with lifting sanctions on Russia. The US and European Union have imposed sanctions on Russian Federation over that move as well as the country's support for separatist rebels in eastern Ukraine. This does not constitute outreach by Mr. Manafort to the President.
Paul Manafort has been accused of lying about his sharing of polling data from 2016 with a Russian man.
Mr. Mueller's team said last month Manafort lied about his connection with Mr. Kilimnik and a wire transfer to a company he was working with.