President Trump has not asked to meet Pope Francis during his visit to Italy next month for the Group of Seven summit, sources said on Tuesday, in what would be a highly unusual omission.
Mr. Trump, who Pope Francis suggested was "not Christian" if he wanted a wall on the Mexican border, is due in Sicily on May 26-27 for a meeting of the heads of the world's richest nations.
The two men have diametrically opposing positions on immigration, refugees, climate change and unbridled capitalism. Trump called the pope's criticism of his plan to build the Mexico wall "disgraceful."
US presidents have in the past made a beeline for the Vatican while they were in Italy or Europe in order to meet with the head of the world's largest Christian church. Only one of them, John Kennedy, was a Roman Catholic.
President George W. Bush met with a pope six times, three times each with Pope John Paul and Pope Benedict.
"The situation can change but are only six weeks left so it looks unlikely at this point," said a diplomat, who spoke on the condition of anonymity.
A senior Vatican diplomatic source confirmed that the White House had so far made no approaches to the Holy See about a possible meeting, which would be the first between the two men.
"The ball is on their side," said another Vatican source. "We have received no request."
A spokesperson for the US Embassy to the Vatican had no comment.
As a matter of policy, popes meet with any head of state who requests an audience, regardless of any differences they have.
Besides being leader of the world's 1.2 billion Roman Catholics, the pope is a head of state. Such meetings allow for an exchange of views on world affairs and a chance for the pope to encourage ethical solutions to world problems.
About 21 percent of Americans, or 70 million people, are Catholic. Washington has had full diplomatic relations with the Vatican since 1984, when President Ronald Reagan saw the Vatican under Pope John Paul, a Pole, as a crucial ally against communism.
Vatican officials have indicated that if the White House wants to squeeze in a meeting with the pope on Trump's schedule in Europe, they will try to oblige. Trump is due to attend a NATO meeting in Brussels on May 25 before going to Sicily for the G7.
Francis visited the United States in 2015 and there are no plans for a return in the foreseeable future, so it is not clear when a meeting between the two men could take place.
Last year, in response to an answer about then-candidate Trump's views on immigration and his intention to build a wall on the border with Mexico, Francis said a man with those views is "not Christian."
Trump, who grew up in a Presbyterian family, shot back saying it was "disgraceful" for the pope to question his faith.
In March, Cardinal Peter Turkson, a close aide of the pope, urged Trump to listen to "dissenting voices" and reconsider his position on climate change, after Trump signed an executive order dismantling Obama-era environmental legislation.
Francis has made defense of the environment a key plank of his papacy, strongly backing scientific opinion that global warming is caused mostly by human activity.