"We will not talk about this until it's over," Giuliani said. "It's the grand jury and grand juries, as I recall, are secret. I'm not going to comment on the grand jury investigation. They ask the questions and we'll see."
On Monday, US corporate media reported that Giuliani has been informed that he is the target of a criminal investigation into election interference in Georgia.
The report said the criminal investigation is related to the 2020 US presidential election and Giuliani was called to testify on the matter.
Giuliani helped lead Trump’s efforts to put under question the results of the 2020 presidential election based on claims of voter and election fraud.
Meanwile, former US Vice President Mike Pence on Wednesday said he would consider testifying before the January 6 investigative committee if asked, but that such an invitation would be unprecedented.
"If there was an invitation to participate, I would consider it," Pence said during an event in New Hampshire when asked whether he would provide testimony to the panel of lawmakers. "It would be unprecedented in history for a vice president to be summoned to testify on Capitol Hill."
The committee, tasked with investigating the events surrounding the breach of the US Capitol on January 6, 2021, has held a series of interviews and public hearings on the matter.
One public hearing focused on an alleged pressure campaign against Pence by former President Donald Trump to get the vice president to stop the certification of election results on January 6. Pence as President of the Senate was responsible for overseeing the certification that day.
Trump denied allegations emerging from the committee that he called Pence a "wimp," but said that the former vice president "did not have the courage to act."
Pence on November 15 is set to release a memoir recounting his time as vice president of the Trump administration. The book will include details about the severing of relations between Trump and Pence following the events of January 6, according to publisher Simon and Schuster.
Trump has roundly condemned the work of the committee and the lawmakers on it, including Representative Liz Cheney. Cheney late on Tuesday conceded defeat to primary election challenger Harriet Hageman, who is backed by Trump.