Negotiations about an interview between President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE and special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE seem to be “down near the end,” Rudy Giuliani told The Hill on Tuesday afternoon.

The president’s lawyer did not slam the door on the idea of such an interview, insisting that “we’re not giving them a straight turndown.”

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He said that the Trump team was not going to agree to everything Mueller’s team wanted but stressed, “I hope it is in the realm of debatable and negotiable.”

Asked about a letter that the Trump team was reportedly preparing in relation to the special counsel’s request for an interview, Giuliani said “We’re writing it.”

“It’ll be done tomorrow — or in the worst case scenario it will be done on Thursday,” Giuliani added.

The question of whether Trump will consent to an interview with Mueller’s team is one of the most critical surrounding the special counsel’s 15-month probe.

Giuliani told Robert Costa of The Washington Post on Monday that he had a “real reluctance about allowing any questions about obstruction.”

Negotiations have been heating up since March, when Mueller’s team suggested it could subpoena the president if he did not submit to an interview.

Trump has been widely reported to favor giving an interview, apparently believing that he will be able to persuade Mueller that he has done nothing wrong.

The president’s lawyers and others in his orbit are skeptical, fearing that Trump could be walking into what they call a “perjury trap.”

In his Tuesday afternoon interview with The Hill, Giuliani expanded on the “perjury trap” idea, contending that the special counsel’s team seemed more inclined to believe former FBI Director James Comey James Brien ComeySteele Dossier sub-source was subject of FBI counterintelligence probe Judge will not dismiss McCabe's case against DOJ Democrats fear Russia interference could spoil bid to retake Senate MORE than the president. He did not state his reason for holding that opinion.

Trump fired Comey in May 2017, a decision that helped precipitate Mueller’s appointment. Comey has said that at a meeting on Feb. 14, 2017, Trump expressed the hope that the FBI could back off Michael Flynn, who had a short-lived tenure as Trump’s national security adviser.

Comey says Trump told him, “I hope you can see your way clear to letting this go, to letting Flynn go. He is a good guy. I hope you can let this go.”

Flynn has subsequently pleaded guilty to lying to the FBI.

Giuliani insisted to The Hill that Comey’s account is false — but that it forms the jaws of the trap into which Trump might walk.

“The answer is not going to change. The answer as to when he asked Comey to go easy — the answer is he did not,” the former New York City mayor said. “Now, if they have Comey saying that he did, the only reason they want [Trump] to say he did not, under oath, is to try to trap him into a perjury prosecution.”

Giuliani added: “I can’t help it if you believe Comey.”

The president has ratcheted up his rhetoric against the Mueller probe of late, referring to it as a “witch hunt” with ever-greater frequency.

Last week, the president called on Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsRoy Moore sues Alabama over COVID-19 restrictions GOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs MORE to “stop this Rigged Witch Hunt right now.”

In a tweet on Sunday morning, Trump admitted that the purpose of a June 2016 Trump Tower meeting — an encounter at which a Russian lawyer met Donald Trump Jr. Don John Trump'Tiger King' star Joe Exotic requests pardon from Trump: 'Be my hero please' Zaid Jilani discusses Trump's move to cancel racial sensitivity training at federal agencies Trump International Hotel in Vancouver closes permanently MORE, then-campaign manager Paul Manafort Paul John ManafortOur Constitution is under attack by Attorney General William Barr Bannon trial date set in alleged border wall scam Conspicuous by their absence from the Republican Convention MORE and Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE — was “to get information on an opponent." Trump continued to insist he knew nothing about the meeting in advance.

To some observers, that tweet could itself be legally problematic for the president or particularly for his son — partly because it is illegal for a campaign to solicit money or other things of value from a foreign national or foreign government, and partly because the tweet casts a shadow over earlier, misleading explanations.

When The New York Times first reported that the meeting had taken place, a statement was issued in Donald Trump Jr.’s name, insisting that it was “primarily … about the adoption of Russian children.”

Figures close to the president, including lawyer Jay Sekulow and White House press secretary Sarah Huckabee Sanders, last year denied that Trump had dictated that statement. But in a memo to Mueller’s team in June, Trump’s lawyers acknowledged that he had, in fact, done so.

Giuliani told The Hill that there was no self-imposed deadline to come to a final answer to Mueller’s request for an interview with the president. But “it feels like” it is moving to a conclusion, he said.

Soon, he added, “we’re going to find out who is going to give on the things that are important.”