The lead U.S. House investigator is predicting the whistleblower who sparked impeachment proceedings against President Donald Trump will testify "very soon."

Intelligence committee chair Adam Schiff said on Sunday news talk shows on NBC and ABC that the panel and the whistleblower's lawyers are still working out their clearances and how to keep the person's identity secret, in talks confirmed by one of the whistleblower's lawyers.

Lawyers continue to work with both parties in the House and Senate, "and we understand and all agree that protecting [the] whistleblower's identity is paramount," lawyer Mark Zaid said in a tweet Sunday.

The person's testimony would be at the heart of a formal inquiry into whether Trump abused his office when he asked Ukraine's president to investigate Democrat Joe Biden's family during a phone conversation.

NEWS ALERT: Re: whistleblower contact w/Congress<br><br>We continue to work w/both parties in House & Senate & we understand all agree protecting whistleblower's identity is paramount. Discussions continue to occur to coordinate & finalize logistics but no date/time has yet been set. —@MarkSZaidEsq

The White House on Thursday released a rough transcript of the July 25 call and made public the whistleblower's complaint. Trump has said he did nothing wrong, but the material sparked new calls for his impeachment and a process that could generate a vote by Thanksgiving.

Trump's lawyer, Rudy Giuliani, appeared on ABC's This Week on Sunday, telling the show he would only co-operate with the House impeachment inquiry if his client, the president, wants him to testify.

Rudy Giuliani, a personal lawyer for Donald Trump, has said he would only co-operate with the House impeachment inquiry if his client, the president, agreed. (Andrew Harnik/The Associated Press)

Giuliani also said he thinks Schiff "has already prejudged" whether Trump linked U.S. aid to Ukraine in exchange for the probe.

"If he decides that he wants me to testify, of course I'll testify, even though I think Adam Schiff is an illegitimate chairman. He has already prejudged the case," Giuliani said.

Schiff has said he hasn't decided whether he wants to hear sworn testimony from Giuliani.

Central to the Democrat-led inquiry is Giuliani's effort to have Ukraine conduct a corruption probe into 2020 presidential candidate Joe Biden and his son Hunter's dealings with a Ukrainian energy company.

The whistleblower expressed concern that U.S. President Donald Trump used 'the power of his office' to solicit foreign help to discredit Democratic presidential hopeful Joe Biden. (Kevin Lamarque/Reuters)

Trump echoed that request in a July call with Ukraine's president that has now led to the impeachment drive examining whether Trump linked U.S. aid to Ukraine in exchange for that probe. There has been no evidence of wrongdoing by either Biden.

For now, Schiff, a Democrat from California, is working to strike a deal with the anonymous whistleblower whose complaint, made in mid-August, forms the heart of the proceedings against the 45th president.

For Trump, the developments pose a threat like none he's encountered before, even from the special counsel Robert Mueller report over Russia's meddling in the 2016 elections. The release last week of a rough transcript of Trump's call with Ukrainian President Volodymyr Zelenskiy and the whistleblower's complaint have put Trump's own words and actions under heightened scrutiny. Democrats are waiting to see how the White House responds to congressional demands for testimony and documents.

Threat of using article of obstruction

"If they're going to obstruct, then they're going to increase the likelihood that Congress may feel it necessary to move forward with an article on obstruction," said Schiff, the committee chair.

While Trump was at his club in Sterling, Va., his former homeland security adviser suggested that Giuliani would be doing the president a disservice by espousing the false story that Ukraine, and not Russia, meddled in the 2016 U.S. elections.

"I am deeply frustrated with what he and the legal team is doing and repeating that debunked theory to the president. It sticks in his mind when he hears it over and over again," said Tom Bossert, who also was an adviser to President George W. Bush. "That conspiracy theory has got to go, they have to stop with that, it cannot continue to be repeated."

'You and I lived through the impeachment of President [Bill] Clinton and saw how frustrating and dividing it could be and I just spend the week overseas and I'll tell you, the whole world is watching,' former Homeland Security adviser Tom Bossert said, speaking to ABC's This Week interviewer George Stephanopoulos. (Kevin Lamarque/Reuters )

Bossert, who is now an ABC News contributor, was speaking to ABC's This Week program.

During his TV appearances, Giuliani not only repeated the allegations but also brandished what he said were affidavits that support them and claimed that Trump "was framed by the Democrats."

Trump, in his July 25 conversation with Zelenskiy, made a brief and cryptic reference to CrowdStrike, a security firm hired by the Democratic National Committee. The DNC's network had been hacked and emails were stolen that were subsequently published by WikiLeaks.

Crowdstrike detected, stopped and analyzed the hack five months before the 2016 election and determined that Russian agents were responsible. Its findings were confirmed by FBI investigators. But conspiracy theorists dispute that and claim the hack is evidence that Trump is being persecuted by "the deep state."

"I would like to find out what happened with this whole situation with Ukraine, they say CrowdStrike ... The server, they say Ukraine has it," Trump says, according to the rough transcript of his call with Ukraine's leader.

The theory espouses that the hack was a setup designed to cast blame on Russia.

Giuliani acknowledged that Ukraine was not to blame for the DNC hack, but that the country peddled misinformation during the campaign.

Bossert, however, said he believes that "this president has not gotten his pound of flesh yet from past grievances on the 2016 investigation," he said of Mueller's investigation. "If he continues to focus on that white whale, it's going to bring him down."

WATCH - From The National, Trump demands to meet whistleblower: