He is wanted in Ukraine on corruption charges.
Leshchenko claimed the alleged 2009 payment to Manafort was backed by a "fake invoice and a fake contract" according to which the American supplied computers to a Belize offshore company. Mr Manafort stepped down from his role in the Trump campaign when the documents surfaced, but claimed all of his dealings in Ukraine were legal.
Serhiy Leshchenko, an investigative journalist who became a member of parliament after Ukraine's 2014 revolution, unveiled the documents just hours after Federal Bureau of Investigation director James Comey said his agency was investigating ties between Russian Federation and the Trump campaign; he declined to identity any individual who was under scrutiny.
Sergiy Leshchenko told reporters in Kiev that Yanukovych's party recorded a secret payment of $750,000 to Manafort in 2009 for "political consulting". The ledger, viewed as a party slush fund, was found at the party headquarters in the turmoil after Ukraine's 2014 revolution.
The ledger, which is now being investigated by the NABU, is believed to be part of Mr Yanufvych's illegal, off-the-books payment system.
Manafort resigned from heading Trump's presidential campaign in August after briefly serving as its campaign manager during the summer of 2016.
Leshchenko alleges that Manafort falsified an invoice to the Belize-based company in order to legitimize the $750,000 payment to himself.
The text messages were part of a large cache released by a hacker group in February that reportedly came from the iPhone of Paul Manafort's daughter Andrea.
"[The FBI is] investigating the nature of any links between individuals associated with the Trump campaign and the Russian government and whether there was any coordination between the campaign and Russia's efforts", Mr Comey said.
Comey declined to comment on the delay during his congressional testimony, but a federal law enforcement official told Politico that participation in mutual legal assistance treaties often takes time to negotiate.
Manafort has previously accused Leshchenko of blackmailing him by threatening to release harmful information about his financial relationship with Yanukovych. Leshchenko has called the exchange a forgery. Mr Manafort, meanwhile, is credited with crafting the strategy that propelled Mr Yanukovych to the presidency in 2010.
Manafort worked for Yanukovych's Party of Regions for almost a decade and helped get the pro-Russian candidate elected in Ukraine in 2010.