His predecessor, the late pope Francis, travelled to France several times but never visited Paris on an official trip.
Pope Leo's visit "could take place at the end of September", the Bishops' Conference of France (CEF) said.
"Under the proposed schedule, Pope Leo XIV could travel to Paris and Lourdes," it said, referring to one of the main Catholic pilgrimage sites.
CEF President Jean-Marc Aveline issued an invitation, and President Emmanuel Macron during his meeting with Pope Leo in Rome last month endorsed it, the CEF said.
The Vatican has yet to confirm any visit.
Pope Leo last month wrapped up a trip to Africa, and is due to visit Spain from June 6 to 12.
The late pope Francis made three trips to France during his 12 years in the post before he died last year, aged 88.
He travelled to Strasbourg in 2014, followed by visits to Marseille in 2023 and Corsica in 2024.
But he never made a state visit to France, insisting instead that his trips were focused on visiting European institutions, among other missions.
He declined Macron's invitation to attend the reopening of Notre-Dame Cathedral in Paris in 2024, five years after a devastating fire.
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