Under new CEO Pietro Labriola, former phone monopoly TIM is seeking an overhaul of its business centred around ceding control of its landline grid to CDP to raise cash and cut its debt pile.
CDP would in turn merge TIM's network assets with those of smaller rival Open Fiber. The state lender, which owns a 60% stake in Open Fiber, is also TIM second largest investor behind French group Vivendi.
However, Alessio Butti, lawmaker and responsible for telecoms policy in Giorgia Meloni's Brothers of Italy, said in a statement that his party was against any plan to sell TIM's infrastructure.
"We need a different scheme that protects TIM's workers, with CDP holding a majority and controlling stake so as to secure the Italian network management," Butti said.
"We are strongly against the plan to sell TIM's landline grid," he added.
Finding a long-term fix for TIM's woes has been a long-running problem for the company and its stakeholders.
Italy's biggest telecoms company is saddled with 24.6 billion euros of net debt while contending with shrinking revenue in its fiercely competitive home market.
The latest plan involves shedding thousands of jobs from a domestic workforce of more than 40,000.
Labriola on Thursday said talks on the single network project had not been halted by the collapse of Prime Minister Mario Draghi's government, which paved the way for snap national election on Sept. 25.
CDP was not immediately available for comment.
In recent weeks, Brothers of Italy has repeatedly asked CDP to stop talks with TIM until a new government is in place.
Under a non binding pact sealed in May, CDP is expected to submit a preliminary bid for TIM's network in the coming weeks, with the aim of clinching a final deal by the end of October, sources have said.
Butti said his party was not opposed to the creation of a single broadband network combining TIM's network assets with those of Open Fiber but the party wanted this to be the focal point of TIM's operations going forward.
(Reporting by Giuseppe Fonte in Rome and Elvira Pollina in Milan; Editing by Keith Weir)
By Giuseppe Fonte and Elvira Pollina