Former New York City Mayor Rudy Giuliani told The Hill on Wednesday that President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE’s legal team was still “several weeks away” from determining whether the president would consent to an interview with 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.

Giuliani, who joined the president’s legal team roughly two weeks ago, said the decision would be determined in large part by how “objective” he and his colleagues perceive Mueller to be.

“The more objective [Mueller] is, the more likely we would be willing to cooperate. The less objective, then we would be foolish to do that,” he said.

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Since joining the president’s team, Giuliani has suggested that Trump would be more likely to sit for an interview if he were persuaded that Mueller and his team had not already concluded that former FBI Director James Comey James Brien ComeyDemocrats fear Russia interference could spoil bid to retake Senate Book: FBI sex crimes investigator helped trigger October 2016 public probe of Clinton emails Trump jabs at FBI director over testimony on Russia, antifa MORE is telling the truth about his interactions with Trump, which are detailed in contemporaneous memos he wrote.

Comey’s version of events is deeply critical of the president, who fired him. Trump, in turn, says Comey is lying.

Skeptics argue that the president’s lawyers are seeking simply to lay a predicate for refusing an interview.

Giuliani and others in and around the president’s legal team insist they are negotiating in good faith, however.

The former New York City mayor spoke to The Hill only hours after it emerged that Ty Cobb would leave his role as the primary White House counsel on the Russia investigation.

Cobb is seen as having favored a more conciliatory approach toward Mueller, believing that this represented the best strategy for bringing the probe to an expeditious conclusion.

White House press secretary Sarah Huckabee Sanders confirmed that Cobb would leave at the end of the month, to be replaced by Emmet Flood. Flood represented President Clinton during his impeachment proceedings.

Cobb had been marginalized of late, with his view perceived to have fallen out of favor.

The president responded with fiery tweets to raids on premises belonging to his longtime attorney Michael Cohen, becoming even more antagonistic to Mueller. Trump allies including erstwhile chief strategist Stephen Bannon were publicly critical of Cobb’s approach. And a number of personnel moves also showed the tide moving against Cobb.

Veteran lawyer John Dowd, who had been leading the president’s outside legal team, departed in March.

In addition to Giuliani’s hiring, the president moved at one point to hire Joe diGenova and Victoria Toensing, a pugnacious husband-and-wife team. Although conflicts stymied that move, it was seen as representative of a shift toward a more confrontational stance.

At the same time as Giuliani was recruited, another husband-and-wife team, Martin Raskin and Jane Serene Raskin, was also brought on board.

Despite the reported tensions, Giuliani paid tribute to Cobb. The existing team of lawyers “have all worked with him longer than me … they feel that he has done a superb job,” he told The Hill.

Giuliani did not endorse the idea that Cobb’s departure and the arrival of Flood and himself marked a shift in strategy. He insisted it was instead a matter of “putting fresh eyes on this to see what can be done to work it out.”

A Washington Post report on Tuesday evening revealed that Mueller had threatened back in March to subpoena Trump if the president did not agree to a voluntary interview. The specter of a subpoena was one that Cobb, in particular, was seen as very eager to avoid.

In a brief phone interview, diGenova — who is understood to provide informal advice to the president though he has no official role in Russia-related matters — insisted that Cobb had “been wanting to leave for a considerable period of time.”

Regarding a possible Mueller-Trump interview, diGenova added, “It all boils down to what Rudy and Mueller are talking about. They are the only ones who know.”

“We certainly know what the president thinks,” diGenova added wryly.

Three times since Monday, Trump has used the phrase “witch hunt” on Twitter to describe the investigation.