"We will be reaching out to the Vatican to see if an audience with the pope can be accommodated," White House spokesman Sean Spicer said. "We would be honored to have an audience with his holiness."
Vatican spokesman Greg Burke said Pope Francis would welcome a request for an audience and do his best to ensure it happened.
"As of the end of last week we had not had an official request for an audience but for sure we would welcome it," Burke told AFP, adding that he did not anticipate any scheduling clashes which could prevent a meeting taking place around the dates Trump is due to be in Italy.
World leaders normally give the Vatican at least several months notice of requests for a papal audience, which are almost invariably granted if logistically possible.
In Trump's case, the request will be coming in barely a month before he is due in Sicily for the G7 summit and after months of will-he, won't-he speculation about a possible meeting centered on the two men's very different world views.
While campaigning in February 2016 to become the Republican Party's nominee for the White House, Trump and the pontiff had a heated and extraordinary exchange through the media.
Trump retorted: "For a religious leader to question a person's faith is disgraceful."
Trump later softened his tone, saying the pope was misinformed, unaware of the impact of the drugs coming into the United States and a range of security issues that made it necessary to build a wall along the southern US border.
On a visit to Mexico in February 2016 Francis held an open-air mass on the US-Mexico border, where he described forced migration as "a human tragedy."
But he also implored the former reality TV star to continue to help those who suffer the most -- "the poor, the outcast and those in need who, like Lazarus, stand before our door.
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