Lawmaker Serhiy Leshchenko said he had evidence that Mr Manafort had tried to hide a payment of $750,000 (Â£600,800) by a pro-Russian party in 2009.
Mr Manafort's spokesman denied the claim as "baseless".
Mr Manafort was an adviser to Ukraine's ex-President Viktor Yanukovych. But he denies receiving any cash payments.
He was forced to resign as Mr Trump's campaign chairman in August 2016 over revelations about his ties to Mr Yanukovych.
Mr Manafort is one of a number of the presidential associates currently under scrutiny for possible contacts with Russia during the US presidential campaign.
On Monday, FBI director James Comey confirmed for the first time that his agency was investigating alleged Russian interference in the election.
On Tuesday, Mr Leshchenko, a former investigative journalist, published an invoice purportedly signed by Mr Manafort that showed a $750,000 payment for a shipment of computers to a firm called Davis Manafort.
The funds came from an offshore company in Belize via a bank in Kyrgyzstan.
Mr Leshchenko said the contract was a cover for payments to Mr Manafort for his consulting services to Mr Yanukovych's Party of Regions.
Mr Leshchenko said the amount and date of the payment matched one of the entries on the so-called Black Ledgers (handwritten accounting books alleged to belong to the Party of Regions), where Mr Manafort's name was mentioned.
Mr Manafort's spokesman Jason Maloni described the latest allegations as "baseless", saying they should be "summarily dismissed".
President Yanukovych was ousted during mass street protests in Ukraine in 2014.
Further allegations have been made in Ukraine about secret funds said to have been paid to Donald Trump's former campaign chairman Paul Manafort.