Crippled by a huge net financial debt burden -- totalling some 25.5 billion euros last September -- TIM has seen stiff price competition steadily erode earnings in its domestic market.

KKR's move comes as government-sponsored talks over a revamp of TIM between TIM's leading investor Vivendi, Italian state lender Cassa Depositi e Prestiti (CDP) and the government went nowhere, hampering CEO Pietro Labriola's plans to revamp the company.

Labriola's strategy is centred around a split of TIM's wholesale landline and submarine network assets from its service operations, with the former assuming a significant portion of the company's debt and staff.

Here is what the various parties are looking for:

KKR

The U.S. investment fund has already spent some 2 billion euros to buy a stake in TIM's last-mile unit FiberCop and wants to preserve returns on its investment, which depend on TIM meeting targets to upgrade its grid from copper to fibre.

TIM said the size of the stake that KKR was seeking was yet to be defined, but the move would result in the U.S. firm taking control of a newly created company comprising TIM's domestic landline network as well as submarine cable unit Sparkle.

TIM did not disclose the value of the non-binding bid but a source familiar with the matter said it valued the infrastructure north of 20 billion euros ($22 billion).

THE GOVERNMENT

Prime Minister Giorgia Meloni's right-wing government wants to maintain the security of TIM's landline grid and its submarine cable unit Sparkle, both deemed strategic.

The government has also said the management of the network should be in state hands as it seeks to protect TIM's 40,000 workers. It can block unwanted interest in Italy's main telecoms infrastructure under so-called golden powers rules.

In November, Meloni's office put on hold a plan sponsored by previous administration led by Mario Draghi envisaging CDP taking over TIM's fixed network assets to combine them with its smaller broadband unit Open Fiber.

CASSA DEPOSITI E PRESTITI (CDP)

Treasury-owned CDP already owns 10% of Telecom Italia. Together with international funds, it was also studying a buyout of TIM's network business, which it values in the region of 17-18 billion euros, including debt.

CDP also owns a 60% stake in TIM's smaller rival Open Fiber, meaning it could combine their infrastructures at a later stage.

Infrastructure fund Macquarie, which hold a 40% stake in Open Fiber, was expected to join any CDP bid.

VIVENDI

After opposing for years the idea of TIM ceding control of its main network asset, top investor Vivendi has warmed to the idea but is seeking a valuation of 31 billion euros to back a sale to CDP.

The French media company has spent about 4 billion euros building its 24% stake since 2015 and faces a theoretical loss of just less than 3 billion euros at TIM's current market value.

Controlled by billionaire Vincent Bollore, Vivendi would exit the infrastructure business to focus on TIM' service operations, which include pay-TV platform TimVision

(Reporting by Elvira Pollina, Valentina Za and Giuseppe Fonte; Editing by Keith Weir)