Military commander Khalifa Haftar, a powerful figurehead in the east of Libya, and Fayez Seraj, head of the U.N.-backed government in Tripoli, will meet with French President Emmanuel Macron in Paris on July 25, al-Hayat newspaper reported.
The two held talks in Abu Dhabi in May, their first in more than a year and a half, about a U.N.-mediated deal that Western powers hope will end the factional fighting that has dominated Libya since the 2011 fall of Muammar Gaddafi.
Citing unidentified sources, Saudi-owned al-Hayat said the meeting sought to build on diplomatic efforts by the United Arab Emirates, the United Nations and neighbouring Egypt.
Macron said on July 13 there would be concrete diplomatic initiatives on resolving the conflict soon.
He wants France to play a bigger role in coaxing Libya's factions to end the turmoil that has allowed Islamist militants to gain a foothold and migrant smugglers to flourish in the absence of a strong central government.
The meeting comes at a time when Haftar has gained ground militarily with Egyptian and United Arab Emirates support, and Western states say Haftar must be part of any solution to the conflict in the oil-producing North African state.
French officials fear Islamic State (IS) militants - who were driven from the coastal city of Sirte last year - and other Islamist militants could try to exploit the power vacuum in Libya to regroup after losing substantial ground in Syria and Iraq, and see this a window to push the sides closer together.
The U.N.-backed Libyan Government of National Accord has sat in Tripoli for more than a year, but has struggled to reach agreement with eastern factions, including Haftar.
Libya's neighbours and regional powers have often differed on how to help. Egypt and the UAE are closer to Haftar and his anti-Islamist militant campaign while Seraj is loosely supported by militias in the west of the vast country that include Islamist groups backed by Turkey and Qatar.
Paris sees its close ties with the leaders of the UAE and Egypt as giving it some leeway in getting all sides on board, especially with the United States showing little interest in getting involved.
Diplomats said a rough plan could see Paris working to refine the U.N. accord by setting up a presidential council that would include Haftar, Seraj and a third actor from the east with Haftar heading up the Libyan National Army.
This would then be rubber-stamped by the U.N. Security Council and pave the way for national elections.
Officials in Haftar's Libyan National Army and Seraj's government did not immediately respond to requests for confirmation. France's foreign ministry and Macron's office said they had no information on the subject.