Ammar Houri, a lawmaker with the Hariri's Future Movement, told Hezbollah's al-Manar news station that Hariri offered to leave the telecommunications ministerial portfolio with opposition leader Michel Aoun, leader of the Free Patriotic Movement.
Hariri, however, objected to the reappointment of caretaker Telecommunications Minister Jebran Bassil, who is Aoun's son-in-law.
The Future Movement lawmaker stressed, however, that nothing is certain as Hariri is expected to meet later this week with Aoun.
Hariri led his March 14 coalition to power in June parliamentary elections, defeating the March 8 opposition slate and promising to form a unity government quickly. Disputes over the appointment of Bassil and political defections undermined his efforts, however, forcing Hariri to step down briefly.
Bassil was not re-elected in June.