One adviser said the president has simply expressed a curiosity in understanding the reach of his pardoning authority, as well as the limits of Mueller's investigation.
"This is not in the context of, 'I can't wait to pardon myself,' " a close adviser said.
With the Russia investigation continuing to widen, Trump's lawyers are working to corral the probe and question the propriety of the special counsel's work. They are actively compiling a list of Mueller's alleged potential conflicts of interest, which they say could serve as a way to stymie his work, according to several of Trump's legal advisers.
A conflict of interest is one of the possible grounds that can be cited by an attorney general to remove a special counsel from office under Justice Department regulations that set rules for the job.
Responding to this story on Friday after it was published late Thursday, one of Trump's attorneys, John Dowd, said it was "not true" and "nonsense."
"The president's lawyers are cooperating with special counsel Robert Mueller on behalf of the president," he said.
A look at President Trump’s first six months in office
Other advisers said the president is also irritated by the notion that Mueller's probe could reach into his and his family's finances.
Trump has been fuming about the probe in recent weeks as he has been informed about the legal questions that he and his family could face. His primary frustration centers on why allegations that his campaign coordinated with Russia should spread into scrutinizing many years of Trump dealmaking. He has told aides he was especially disturbed after learning Mueller would be able to access several years of his tax returns.
Trump has repeatedly refused to make his tax returns public after first claiming he could not do so because he was under audit or after promising to release them after an IRS audit was completed. All presidents since Jimmy Carter have released their tax returns.
"If you're looking at Russian collusion, the president's tax returns would be outside that investigation," said a close adviser to the president.
Further adding to the challenges facing Trump's outside lawyers, the team's spokesman, Mark Corallo, resigned on Thursday. Corallo confirmed Friday that he has resigned but declined to comment further.
Corallo's departure is part of a larger restructuring of Trump's team undertaken in recent days. Marc Kasowitz, Trump's New York-based personal attorney who had been leading the effort, will take a reduced role, people familiar with the team said. Meanwhile, veteran Washington lawyer Dowd, hired last month, will take the lead in responding to the special counsel and congressional inquiries. Jay Sekulow, a lawyer who has been a familiar face in conservative media in recent years, will serve as the group's public face, appearing frequently on television.
Sekulow said in an interview Thursday that the president and his legal team are intent on making sure Mueller stays within the boundaries of his assignment as special counsel. He said they will complain directly to Mueller if necessary.
"The fact is that the president is concerned about conflicts that exist within the special counsel's office and any changes in the scope of the investigation," Sekulow said. "The scope is going to have to stay within his mandate. If there's drifting, we're going to object."
Sekulow cited Bloomberg News reports that Mueller is scrutinizing some of Trump's business dealings, including with a Russian oligarch who purchased a Palm Beach mansion from Trump for $95 million in 2008.
"They're talking about real estate transactions in Palm Beach several years ago," Sekulow said. "In our view, this is far outside the scope of a legitimate investigation."
The president has long called the FBI investigation into his campaign's possible coordination with the Russians a "witch hunt." But now, Trump is coming face-to-face with a powerful investigative team that is able to study evidence of any crime it encounters in the probe — including tax fraud, lying to federal agents and interference in the investigation.
"This is Ken Starr times 1,000," said one lawyer involved in the case, referring to the independent counsel who oversaw an investigation that eventually led to House impeachment proceedings against President Bill Clinton. "Of course, it's going to go into his finances."
Following Trump's decision to fire FBI Director James B. Comey — in part because of his displeasure with the FBI's Russia investigation — Deputy Attorney General Rod J. Rosenstein appointed Mueller as special counsel in a written order. That order gave Mueller broad authority to investigate links between the Russian government and the Trump campaign, as well as "any matters that arose or may arise directly from the investigation" and any crimes committed in response to the investigation, such as perjury or obstruction of justice.
Mueller's probe has already expanded to include an examination of whether Trump obstructed justice in his dealings with Comey, as well as the business activities of Jared Kushner, Trump's son-in-law.
Trump's team could potentially challenge whether a broad probe of Trump's finances prior to his candidacy could be considered a matter that arose "directly" from an inquiry into possible collusion with a foreign government.
The president's legal representatives have also identified what they allege are several conflicts of interest facing Mueller, such as donations to Democrats by some of his prosecutors.
Another potential conflict claim is an allegation that Mueller and Trump National Golf Club in Northern Virginia had a dispute over membership fees when Mueller resigned as a member in 2011, two White House advisers said. A spokesman for Mueller said there was no dispute when Mueller, who was FBI director at the time, left the club.
Trump also took public aim on Wednesday at Attorney General Jeff Sessions and Rosenstein, whose actions led to Mueller's appointment. In an interview with the New York Times Wednesday, the president said he never would have nominated Sessions if he knew he was going to recuse himself from the case.
Some Republicans in frequent touch with the White House said they viewed the president's decision to publicly air his disappointment with Sessions as a warning sign that the attorney general's days were numbered. Several senior aides were described as "stunned" when Sessions announced Thursday morning he would stay on at the Justice Department.
Another Republican in touch with the administration described the public steps as part of a broader effort aimed at "laying the groundwork to fire" Mueller.
"Who attacks their entire Justice Department?" this person said. "It's insane."
Law enforcement officials described Sessions as increasingly distant from the White House and the FBI because of the strains of the Russia investigation.
Traditionally, Justice Department leaders have sought to maintain a certain degree of autonomy from the White House as a means of ensuring prosecutorial independence.
But Sessions's situation is more unusual, law enforcement officials said, because he has angered the president for apparently being too independent while also angering many at the FBI for his role in the president's firing of Comey.
As a result, there is far less communication among those three key parts of the government than in years past, several officials said.
Currently, the discussions of pardoning authority by Trump's legal team are purely theoretical, according to two people familiar with the ongoing conversations. But if Trump pardoned himself in the face of the ongoing Mueller investigation, it would set off a legal and political firestorm, first around the question of whether a president can use the constitutional pardon power in that way.
"This is a fiercely debated but unresolved legal question," said Brian C. Kalt, a constitutional law expert at Michigan State University who has written extensively on the question.
The power to pardon is granted to the president in Article II, Section 2, of the Constitution, which gives the commander in chief the power to "grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment." That means pardon authority extends to federal criminal prosecution but not to state level or impeachment inquiries.
No president has sought to pardon himself, so no courts have reviewed it. Although Kalt says the weight of the law argues against a president pardoning himself, he says the question is open and predicts such an action would move through the courts all the way to the Supreme Court.
"There is no predicting what would happen," said Kalt, author of the book, "Constitutional Cliffhangers: A Legal Guide for Presidents and Their Enemies." It includes chapters on the ongoing debate over whether presidents can be prosecuted while in office and on whether a president can issue a pardon to himself.
Other White House advisers have tried to temper Trump, urging him to simply cooperate with the probe and stay silent on his feelings about the investigation.
On Monday, lawyer Ty Cobb, newly brought into the White House to handle responses to the Russian probe, convened a meeting with the president and his team of lawyers, according to two people briefed on the meeting. Cobb, who is not yet on the White House payroll, was described as attempting to instill some discipline in how the White House handles queries about the case. But Trump surprised many of his aides by speaking at length about the probe to the New York Times two days later. Cobb, who officially joins the White House team at the end of the month, declined to comment for this article.
Some note that the Constitution does not explicitly prohibit a president from pardoning himself. On the other side, experts say that by definition a pardon is something you can only give to someone else. There is also a common-law canon that prohibits individuals from serving as a judge in their own case. "For example, we would not allow a judge to preside over his or her own trial," Kalt said.
A president can pardon an individual at any point, including before the person is charged with a crime, and the scope of a presidential pardon can be very broad. President Gerald Ford pardoned former president Richard M. Nixon preemptively for offenses he "committed or may have committed" while in office.
Devlin Barrett and Sari Horwitz contributed to this report.