The range of possible issues up for discussion during the May 24 tête-à-tête is vast.
Although Pope Francis said Saturday he will not be seeking to soften U.S. President Donald Trump's policies during their meeting next week, the encounter is doubtless a rare opportunity for a global moral voice to influence a leader who keeps an unusually tight circle of advisors.
The range of possible issues up for discussion during the May 24 tête-à-tête is vast. Francis could compare Trump's withdrawing of federal environmental regulations with his 2015 ecological encyclical Laudato Si'. Or the pontiff could sharpen his earlier public critique of the planned U.S.-Mexico border wall.
"The significance of this meeting can't be understated," said Douglas Kmiec, a Republican who served as former President Obama's first ambassador to Malta. "Francis could change the course of the times that we live in."
While it is unknown just what the pope might choose to tell the president, Kmiec and three former U.S. ambassadors to the Holy See told NCR in interviews they expect the pontiff to take advantage of the opportunity before him in what is expected to be a half-hour encounter. They also said they hope Trump does the same.
Francis Rooney, who served as Holy See ambassador under George W. Bush from 2005-08, said he would advise Trump to recognize he can "take advantage [of] Vatican diplomacy, particularly the soft power influence it wields in the world."
"I would urge the president to focus on areas where the United States' interest and the Holy See's interest align to promote common foreign policy objectives," said Rooney, now a Congressman from Florida.
Ken Hackett, Obama's last Holy See ambassador, said he would advise Trump to use the opportunity not to speak but to listen. "I would suggest to him that the pope listens well and he should listen to the pope well," said Hackett, who served in Rome from 2013-17.
"That boastfulness that we see all the time with President Trump, I don't think is going to fly well with the Holy Father," he continued. "I would suggest a little more humility."
Trump isn't exactly known for his humility, or for his ability to take advice. Those tendencies were in part a cause of a few days of high tension between him and Francis in 2016.
First, the president called the pope "a political person" for celebrating a Mass near the U.S.-Mexico border. Then, Francis questioned Trump's Christianity over his support for a wall on that border. Later, Trump called the pope's remark about him "disgraceful."
Kmiec, who served in Malta from 2009-11 and is now a professor of constitutional law at Pepperdine University, said Francis "made his point plain that the Christian view that doesn't welcome the stranger is not particularly Christian."
"I think if the two men are going to be going right to the heart of the matter, they might want to start their conversation right where it left off," he suggested.
James Nicholson, who served as George W. Bush's first Holy See ambassador from 2001-05, said he thinks Trump and Francis have to do some "fence-mending" after their 2016 exchange.
"That's kind of a false start together," said Nicholson, who also said he had been contacted by the Trump administration for advice about whether to seek a meeting with the pope around the time of the president's trip to Sicily for a G7 summit May 26-27.
"They need to get that behind them and I think they certainly should talk about immigration," said the former ambassador. "That's one of those issues about which they probably have some disagreement as well as things like capital punishment and climate change. But there's so many things they will have to talk about that they carry in common."
Hackett said that before Obama's meeting with Francis in March 2014 the White House turned to Washington Cardinal Donald Wuerl to ask about what issues the president might most profitably raise with the pope.
"Hopefully, the Trump White House will do the same ... figuring out what topics would resonate," said Hackett.
Trump will meet Francis as part of the first foreign trip of his presidency. He is first visiting Saudi Arabia and Israel, and then heading to a NATO meeting in Brussels before the G7 summit.
During the press conference on the papal flight from Portugal May 13, Francis said he would focus in his meeting with Trump on finding even little openings where the two might have common interests and can work together.
The pope said he will be "searching for the doors that are at least a bit open, entering and speaking of things in common and going ahead, step by step."
Each of the ambassadors said that beyond discussions of any specific set of policies, the real opportunity for the encounter lies in letting the pope and the president get to know each other personally.
Kmiec said developing a personal relationship is "important in a tangible, pragmatic way so that in the event that the world faces a crisis on any given morning ... a phone call can have a positive effect."
"I think it's even more important with this president than with past presidents," he added.
Nicholson, who helped organize three visits by Bush to meet John Paul II, agreed.
"It's recognized that we're not going to bring peace and freedom and order to this world purely with material and military means," he said. "It has to be done through a moral transformation. That's where the pope is so important. That's why the two need to know each other and work together."
Hackett also agreed, but added: "You don't make a relationship in a one-off and there's already been some water over the bridge."
Presidential visits to the Vatican are normally very structured. In the past, the White House has sent several preparatory teams over a period of months in advance of presidential visits to pin down every last detail.
Hackett recalled that before Obama's meeting the administration's security officials even rode up and down the elevators the president would be using in the Vatican's apostolic palace.
But it's unclear just what preparation Trump's team has been able to do. The president has yet to appoint a new Holy See ambassador and he only announced his visit with Francis May 4, giving the Vatican and White House staffs just 20 days to finalize preparations.
To make matters worse, Hackett said that when he left his post January 20 the U.S. embassy was short-staffed, with two primary staffers attending to a lot of the work.
One specific thing the administration has to do in the coming days is pick a gift Trump will present to Francis during the traditional exchange of gifts the pope has in meetings with heads of state. Obama gave Francis a wooden chest containing fruit and vegetable seeds that had been used in the White House Garden.
Hackett suggested the Trump administration stay away from offering anything too fancy.
"That's delicate," he said. "I know that other ambassadors have really suffered when they are not consulted and the head of state brings in some big, giant thing that's totally inappropriate, made of gold or silver."
In the end, Kmiec said he thought Francis might actually be able to influence Trump.
"Whatever length of meeting they've allowed for is going to be insufficient to cover the topic areas," he said. "But what will be sufficient is the power of the Holy Father to just put the president at ease and to speak to his heart."
The former ambassador said the pope has a wealth of kindness that he exhibits "at all times."
"I think that will have a transformative effect on the hardest heart in the room," said Kmiec. "I also think it will have a transformative effect on the president even more than he realizes and more than we can put into words."
Measuring that transformative effect, however, might be difficult. The Vatican normally releases only brief descriptions about the pope's meetings with world leaders, leaving unknown what was actually spoken about.
Some heads of state have been known to exaggerate what the pope told them. "What you should watch is what the White House puts out [afterwards]," Hackett advised. "The question is how much is real and how much is imagined."