The move shows that the former mayor of New York is again putting pressure on the country to investigate the political enemies of President Donald Trump. Giuliani, who serves as Trump's personal attorney, has spent a long time investigating the former vice president's request in 2016 to remove the country's top prosecutor, who once investigated a Ukrainian natural gas company with Biden's son Hunter was in touch.
Other Western governments have also called for this prosecutor's dismissal, and there is no evidence that Biden's move was inappropriate.
The New York Times first reported on Giuliani's talks with Andriy Yermak, whom he called the lawyer of Ukrainian President Volodymyr Zelensky, and wanted to meet with him. Yermak was named advisor to Zelensky in May, according to local media reports.
The two spoke on the phone twice, with Yermak offering to come to the US to meet with Giuliani before the two agreed to meet in Madrid last month, Giuliani said.
Giuliani claims that Yermak had asked him questions and that he did not ask the Ukrainian lawyer to do anything because he "did not have to". The focus of her conversation was on Biden's possible role as then vice president in dismissing the prosecutor and attempting to damage Trump's election campaign, said Giuliani.
Giuliani said he was not worried about how the meeting would be held.
"I would not do anything unethical in my life, I'm a really good lawyer," said Giuliani. "I'm proud of what I did."
He also claimed that he was not prosecuting the matter at the behest of President Donald Trump. CNN has asked the State Department for comments.
Giuliani has been following direct Ukrainian investigations into American politics since the spring. In May, Giuliani traveled to Ukraine to meet with Zelensky to persuade the country to investigate Biden, as well as issues relating to the release of negative information about Paul Manafort, former chairman of the 201
6 Trump campaign. But in the end he reversed the course and decided not to leave.
He told CNN's Michael Warren that he would not meet with the elected president of Ukraine because "the meeting would have done little and could be in the hands of those who could misrepresent it."
Later in This month the Washington Post reported that Giuliani met with a former Ukrainian diplomat who had previously made "unsubstantiated claims that the Democratic National Committee had worked with the Kiev government in 2016 to collect incriminating information."
Michael Warren of CNN contributed to this story.