US President Donald Trump and Saudi Deputy Crown Prince and Minister of Defence Mohammed bin Salman meet at the White House in Washington, US, March 14, 2017. PHOTO: REUTERS
Such a trip is "being discussed," the official said, speaking on condition of anonymity.
Trump invites Modi to visit US later this year
Trump is already planning to attend a NATO summit in Brussels on May 25 and travel to Sicily for a Group of Seven leaders' summit scheduled for May 26-28.
Defense Secretary James Mattis was in Riyadh on Wednesday meeting with senior Saudi officials. He said he hopes his trip could potentially open the door for Trump to visit Saudi Arabia.
Former President Barack Obama met leaders of the six-nation Gulf Cooperation Council, Saudi Arabia, Qatar, the United Arab Emirates, Kuwait, Bahrain and Oman about a year ago.
Trump has made the Middle East and the fight against Islamic State a focus of his young presidency. He ordered the US Navy to fire cruise missiles at a Syrian airfield after a chemical weapons attack in Syria earlier this month.
Saudi Arabia's powerful Deputy Crown Prince Mohammed bin Salman met Trump in Washington in March in a visit that was touted by a senior Saudi adviser as one that hailed a "historical turning point" in US-Saudi relations.
Riyadh had an often fraught relationship with the Obama administration, especially in the wake of the 2015 Iran nuclear deal.
Pentagon enjoying greater leeway under Trump
Saudi Arabia felt the Obama administration considered Riyadh's alliance with Washington less important than negotiating the deal to rein in Iran's nuclear program.
White House spokesman Sean Spicer said it is possible a Trump visit to the Vatican to meet Pope Francis will be added to the schedule of his European trip.
"We'll be reaching out to the Vatican" to see if a visit can be arranged, Spicer told reporters.
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