As reported by Censor.NET, Giuliani, who met with Poroshenko in Ukraine late last year, told Business Insider in a Wednesday phone interview he did not know anything about the reported payment to Cohen, the longtime personal lawyer of the president.
But the attorney added he had "no reason not to believe" Cohen.
"Payments can be proved pretty easily, so it would be silly to deny it if it happened," Giuliani said. "And he never registered as a foreign agent. And as far as I know, never acted as one."
Giuliani said he wanted to "wait for all the facts" to come out in the matter, and that he wasn't going to "get angry" at Cohen over any "hypothetical" situation.
"I have to assume that maybe there was a discussion of doing this," he said of such an arrangement between Cohen and the Ukrainian government. "And on neither end was it consummated."
Citing sources close to those involved, the BBC said the payment was set up by people acting on behalf of Ukrainian President Petro Poroshenko. Cohen was not registered as a representative of Ukraine, which would be required under the Foreign Agents Registration Act if such a payment took place.
The BBC said the payment, which Cohen denied, was made ahead of Poroshenko's White House visit last June. Shortly after Poroshenko returned to Ukraine, the BBC reported, the nation's anticorruption agency pumped the brakes on its investigation into Trump's former campaign manager Paul Manafort, who has since been indicted in the U.S. as part of the special counsel Robert Mueller's Russia investigation.
A high-ranking Ukrainian intelligence officer told the BBC that, before Poroshenko's White House visit, Cohen was brought in because the country's lobbyists couldn't secure a substantive Oval Office meeting with Trump. One source told the BBC that Cohen was paid $400,000, while another said he was paid $600,000.
The BBC wrote that there was no suggestion that Trump knew of the payment.
In addition to Cohen, two Ukrainians who the BBC's sources said opened a back channel with him on behalf of Poroshenko denied the story. The senior Ukrainian intelligence official also told the BBC that Cohen was assisted by a former Trump business partner named Felix Sater, whose lawyer denied the story to the BBC.
After the story was published, Poroshenko's office ripped the claims as "blatant lie, slander, and fake."
"This is how we perceive the disinformation as if the meeting of the President Ukraine and the President of the U.S. had been organized for money,"the statement read. "Ukraine-U.S. summit in June 2017 had been arranged exclusively by means of official diplomatic channels, in particular Ukraine's Embassy in the U.S."
Cohen's lawyer did not immediately respond to a request for comment from Business Insider.