Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., has offered President Trump’s personal attorney, Rudy Giuliani, a chance to come before lawmakers to detail his allegations about former Vice President Joe Biden and his dealings with Ukraine.

“Have heard on numerous occasions disturbing allegations by [Giuliani] about corruption in Ukraine and the many improprieties surrounding the firing of former Prosecutor-General Viktor Shokin,” Graham said Tuesday on Twitter. “Therefore I will offer to Mr. Giuliani the opportunity to come before the Senate Judiciary Committee to inform the committee of his concerns.”

Giuliani told Fox News on Tuesday he intends to testify, but needs to go over the offer with the other attorneys involved to determine whether they could sort out issues regarding attorney-client privilege and executive privilege. “It would be an excellent opportunity to put out in one place at one time all of the evidence and show where the holes are,” he said.

Giuliani, who has been one of the key figures at the center of the House impeachment inquiry into Trump, has accused Biden’s son, Hunter, of improper activity related to his past lucrative board position with energy company Burisma Holdings. He has questioned whether the then-vice president used his office to pressure the Ukrainian government into firing Shokin, who had been investigating Burisma.

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Biden has publicly acknowledged that he pressured Ukraine to fire Shokin, but insisted this was due to corruption concerns and not connected to his son’s business dealings in the country. Biden allies argue this was in line with pressure from other foreign leaders to fire the prosecutor.

The U.S. had support internationally for its opposition to Shokin. Current Ukrainian officials are looking into the handling of the Burisma case but have not accused the Bidens of any wrongdoing. The Wall Street Journal also reported last month that by the time of Biden's intervention, the Burisma probe had been dormant.

Fox News, however, obtained last week a copy of Giuliani’s notes from an interview he conducted in January with Shokin in which the ex-prosecutor claimed that his “investigations stopped out of fear of the United States.”

“Mr. Shokin attempted to continue the investigations but on or around June or July of 2015, the U.S. Ambassador Geoffrey R. Pyatt told him that the investigation has to be handled with white gloves, which according to Mr. Shokin, that implied do nothing,” the notes from the interview stated. The notes also claimed Shokin was told Biden had held up U.S. aid to Ukraine over the investigation.

Trump, too, is accused of holding up aid in order to extract an investigation from Ukraine regarding the Bidens, though he denies any such quid pro quo was at play.

The interview purportedly conducted by Giuliani took place on Jan. 23, 2019 at an office on Park Avenue in New York City. Shokin was interviewed over the phone, and interpreters were used — one in Ukraine and one in New York, according to the notes obtained by Fox News.

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In a statement to Fox News, Giuliani said the details were gathered before Biden announced his presidential run, and the allegations were brought to him.

"I explored them as part of my duty as an attorney to show that the crimes committed, were not by my client, but by Democrats. I was not seeking to investigate Joe Biden. I was not investigating Joe Biden," Giuliani said.

The Biden campaign has slammed Giuliani and blasted media outlets for giving him air time. The campaign wrote to NBC News, CBS News, Fox News and CNN to voice “grave concern that you continue to book Rudy Giuliani on your air to spread false, debunked conspiracy theories on behalf of Donald Trump.”

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“The substance of President Trump and Rudy Giuliani’s claims has been roundly discredited,” Biden Deputy Campaign Manager Kate Bedingfield said last week. “This is not a claim from the campaign or Joe Biden. This is an irrefutable fact.”

Giuliani’s corruption claims against Biden have become a major talking point among Trump’s allies as the president faces an impeachment inquiry following a whistleblower complaint about a July phone call Trump had with Ukrainian President Volodymyr Zelensky during which he asked the Ukrainian leader to investigate the Bidens. House lawmakers are investigating whether Trump’s request was tied to the dispersal of military aid to Ukraine.

Fox News’ John Roberts, Brooke Singman and The Associated Press contributed to this report.