Giuliani, a former Republican mayor of New York City, said that he believed he would be "walking into a group of people that are enemies of the president, and in some cases, enemies of the United States and in one case, an already convicted person who has been found to be involved in assisting the Democrats with the 2016 investigation.
"There was a great fear that the new [Ukrainian] president would be surrounded by, literally, enemies of the president [of the United States] who were involved in that and people who are involved with other Democratic operatives," he told host Shannon Bream.
"I'm convinced from what I've heard from two very reliable people tonight that the president [Ukrainian President-elect Volodymyr Zelensky] is surrounded by people who are enemies of the president [Trump], and people who are -- at least [in] one case -- clearly corrupt and involved in this scheme," Giuliani said.
Giuliani said that his decisions had nothing to do with the upcoming 2020 U.S. presidential election.
Bream asked about "pushback" Giuliani received for announcing his original decision to go, including from U.S. Sen. Chris Murphy, D-Conn., who demanded that the Senate Foreign Relations Committee open an inquiry into the situation.
"Rudolph Giuliani, the President’s personal lawyer, has apparently held meetings with Ukrainian officials in the United States and plans to travel to Ukraine for further discussions," Murphy wrote, in a letter to committee chairman Sen. James Risch, R-Idaho, according to NBC News.
"As far as we know, none of these meetings are being coordinated with the U.S. State Department or other government agencies," Murphy wrote.
Giuliani said that he would welcome Murphy's proposed hearing, saying that he could lay out what he said was alleged "unbelievably incriminating evidence about members of the [Democratic National Committee], members of the Clinton campaign who were involved in gathering information there that was negative to the Trump campaign."
The former mayor also pointed to evidence that 2020 hopeful and former Vice President Joe Biden improperly pressured Ukrainian President Petro Poroshenko and the country's parliament to fire Prosecutor General Viktor Shokin, in March 2016.
At the same time, Biden's son, Hunter, served on the board of the Ukrainian natural gas firm Burisma Holdings -- which was owned by an oligarch, Mykola Zlochevsky, who in turn was being investigated by that same prosecutor.
Shokin was soon voted out by the Ukrainian parliament. After leaving office, Biden admitted on video that he had threatened that the U.S. would pull $1 billion in loan guarantees unless Shokin was terminated.
"That stinks, the facts are stubborn, and eventually this is going to have to be investigated," Giuliani said, adding that in order to prevent any "political suggestions" he is going to "step back and just watch [the situation] unfold."
Fox News' Gregg Re contributed to this report.