CDP, which owns 50 percent of wholesale broadband company Open Fiber, has just under 5 percent of TIM.
Speaking at the presentation of the lender's 2019-2021 business plan, Tononi said a government proposal to create a single fast broadband operator was "reasonable".
He said investing in two separate networks would be a waste of resources. But he added the creation of a single network would depend on the companies involved.
The Italian government has introduced measures to help create a single broadband infrastructure company that could combine the networks of TIM and Open Fiber, which is 50 percent owned by utility Enel.