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 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.