It would be only their second meeting. Their first, in Cuba in 2016, was the first between a pope and a leader of the Russian Orthodox Church since the Great Schism that split Christianity into Eastern and Western branches in 1054.
Kirill, 75, has given his full-throated blessing for Russia’s invasion of Ukraine, a position that has splintered the worldwide Orthodox Church and unleashed an internal rebellion that theologians and academics say is unprecedented.
The sources, who spoke on condition of anonymity, said the plan was for the 85-year-old pope, who is due in Lebanon on June 12-13, to fly to Amman, Jordan on the morning of June 14.
From there, he would board a helicopter to Jerusalem on the same day for the meeting with Kirill and then return to Rome from there, the sources said.
One source said the trip appeared to be almost certain, while the other said it was one possibility.
Returning from his trip to Malta last week, Francis said he hoped to meet Kirill somewhere in the Middle East this year but did not say where.
Kirill called on Russians on Sunday to rally around the authorities as Moscow pursues what it calls a “special military operation” in Ukraine.
The patriarch has previously made statements defending Moscow’s actions in Ukraine and views the war as a bulwark against a liberal Western culture that he considers decadent.
“Let the Lord help us unite during this difficult time for our Fatherland, including around the authorities,” the Interfax news agency quoted Kirill as saying at a sermon in Moscow.
Russia sent tens of thousands of troops into Ukraine on Feb. 24 to degrade its southern neighbour’s military capabilities and root out people it called dangerous nationalists.
Francis has already rejected that terminology, calling it a war.
Since the war began, Francis has only mentioned Russia explicitly in prayers, such as during a special global event for peace on March 25. But he has made clear his opposition to Russia’s actions, using the words invasion, aggression and atrocities.
On Sunday, the pope called for an Easter truce in Ukraine, and in an apparent reference to Russia, questioned the value of planting a victory flag “on a heap of rubble”.
(Reporting by Philip Pullella; editing by Gareth Jones)