Zain Chief Executive Saad al Barrak confirmed that shareholders were in talks but declined to offer details or to comment whether the talks were with India's Reliance Communications.
Zain is the Gulf Arab region's second-largest telecoms firm by market value. Al-Arabiya did not offer a source or further details.
Barrak said last week that Zain, whose shareholders voted to scrap individual ownership limits on Aug 31 amid a restructuring, was in negotiations to sell a stake in its African business.
Removing the ownership cap on the group means any local or foreign investor would be free to bid for control of the firm as a whole.
Two banking sources told Reuters in August that India's Reliance Communications had started talks to buy Zain's African operations.
The offer of 2 dinars per share reported by Al-Arabiya represents a 28 percent premium to Sunday's closing price of 1.56 dinars and values the stake at 3.93 billion Kuwaiti dinars ($13.68 billion), according to Reuters calculations.
Zain shares rose 5.4 percent on Sunday on the heels of a 20 percent rise in the past month as speculation of a bid has intensified.
Zain said on July 20 it was reviewing a possible sale of its African operations, excluding Morocco and Sudan, after French media and telecom conglomerate Vivendi
Zain's biggest shareholders are Kuwait's sovereign wealth fund, the Kuwait Investment Authority, which owns 24.608 percent and family-owned conglomerate, the Kharafi Group, which holds at least a 10.86 percent stake, according to the Kuwaiti bourse website. Analysts estimate Kharafi owns about 20 percent in Zain through its units.