TIM and Open Fiber have been discussing possible network cooperation, including a possible merger, for several months.
"In coming months we will discuss things with our board and with our shareholders to see what the next steps will be," TIM CEO Luigi Gubitosi said on the sidelines of a conference in Florence, adding that a merger would be positive.
Italy is pushing to create a single ultrafast broadband operator by merging Telecom Italia network with smaller rival Open Fiber to avoid duplicating investments.
Italian State lender Cassa Depositi e Prestit (CDP), which recently became TIM second largest shareholder, co-owns Open Fiber alongside state controlled utility Enel.
The future of TIM’s copper and fiber network has become a key bone of contention between the phone incumbent's top shareholders, France's Vivendi and activist fund Elliott.
Elliott wants TIM to spin off its network and merge it with Open Fiber while Vivendi, though not opposed to a merger, insists TIM keep control of its biggest asset.
(Reporting by Silvia Ognibene; Writing by Stephen Jewkes and Elvira Pollina; Editing by Francesca Landini and Edmund Blair)