"I have never received a single 'off-the-books cash payment,'" Paul Manafort said in a statement.
The New York Times reported finding ledgers pledging $12.7m (£9.8m) in undisclosed cash payments to Mr Manafort between 2007 and 2012.
Hillary Clinton's campaign has called for Mr Trump's team to disclose any pro-Russia links.
"The simplest answer is the truth: I am a campaign professional. It is well known that I do work in the United States and have done work on overseas campaigns as well. I have never received a single 'off-the-books cash payment' as falsely 'reported' by the New York Times," the statement reads.
The New York Times article said Mr Trump's campaign manager and his business played a key role in advising Ukraine's former pro-Russian President Viktor Yanukovych, who fled after an uprising in November 2013.
Mr Manafort's work advising Mr Yanukovych's pro-Russia political party, ended when the country's parliamentary elections were held in 2014, he said in his statement.
The New York Times report said Ukraine's National Anti-Corruption Bureau had discovered the listed payments in the ledgers of Mr Yanukovych's then governing Party of the Regions - allegedly part of "an illegal off-the-books system".
The bureau is also investigating business deals worth millions of dollars put together with the help of Mr Manafort's business.
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