Washington(CNN) Rudy Giuliani is considering re-entering the impeachment fray by launching a podcast to provide impeachment analysis of the public hearings in the House of Representatives scheduled for later this week.

Giuliani was overheard discussing the plans with an unidentified woman while at a crowded New York City restaurant, Sant Ambroeus, over lunch on Saturday. The conversation, which lasted more than an hour, touched on details including dates for recording and releasing the podcast, settling on a logo, and the process of uploading the podcast to iTunes and other podcast distributors.

Two people who overheard Giuliani's discussion reached out to CNN and provided a recording they decided to make of the conversation. They contacted CNN unprompted after reading a recent story about Giuliani and the President's ongoing relationship. The people asked not to be identified and provided the audio recording on the condition that it not be published.

"Many Americans want to hear directly from Rudy Giuliani," said Christianné Allen, a spokeswoman for Giuliani, who confirmed to CNN that he discussed the podcast idea at lunch on Saturday. "He is considering several options, in consultation with Jay Sekulow and the legal team, regarding the best way to move forward. As of now, they have not decided on the strategy but are getting very close."

In the conversation, Giuliani said he hoped to have four or five episodes "to analyze the impeachment in every aspect." Giuliani's intention seems to be to have four episodes finished before the start of the Senate trial.

Giuliani also mentioned two op-eds for major newspapers he was planning on publishing, the first of which would explain why Trump is "unimpeachable" and the second offering an explanation of Giuliani's defense of his client, the President.

Despite his central role in the events surrounding the impeachment inquiry, Giuliani has remained relatively silent since the October arrest and indictment of two of his associates, Lev Parnas and Igor Fruman. He briefly re-emerged on Friday in an appearance on a separate impeachment-focused podcast hosted by former Trump White House official Steve Bannon. In that interview, Giuliani offered his own political analysis of impeachment, saying that some Democrats who vote for articles of impeachment in the House could lose their seats in 2020.

Closed-door testimony from multiple witnesses describes Giuliani as a key facilitator of conversations and actions that have led to the impeachment probe. This week, public testimony from several of those witnesses, including former Ukraine ambassador Marie Yovanovitch, senior State Department official George Kent and Bill Taylor, the top diplomat in Ukraine following Yovanovitch's removal, is expected to further highlight Giuliani's central role. Giuliani has said his actions were all done as part of his legal defense of Trump.

During his conversation on Saturday, Giuliani talked about using the podcast as a way to tell his side of the story and counter-balance the first public televised testimony of the House's impeachment inquiry.

A person close to Trump's legal team suggested the podcast would be a smart counter-move as the hearings will dominate news coverage.

But the podcast could also be risky to the former New York mayor. Federal prosecutors in New York are scrutinizing Giuliani's business dealings with Parnas and Fruman. Both men have emerged as key players in Giuliani's efforts to get the Ukrainian government to investigate Trump's political opponents, including former Vice President Joe Biden and his son Hunter. There is no evidence of wrongdoing by either Biden.

Giuliani has served Trump's legal team primarily by defending the President in media appearances and interviews, first focused on the special counsel investigation into Russian interference and now on the impeachment inquiry.