* TIM Brasil may be worth three times market value - Fossati
Break-up sale is Telefonica's preferred option - sources
* Telecom Italia shares up 10 percent this month
By Danilo Masoni
MILAN, Jan 14 (Reuters) - Dissident Telecom Italia investor Marco Fossati has stepped up efforts to prevent a fire sale of TIM Brasil, declaring that it could be worth more than $40 billion, nearly three times its market value.
The Brazilian wireless carrier is Telecom Italia's main source of growth but has become the focus of a shareholder dispute over how the Italian telecoms group should cut debt and fund much-needed domestic investment.
"In evaluating any possible acquisition proposal, the board will have to operate very carefully," Fossati, whose 5 percent makes him Telecom Italia's third-biggest investor, said in a letter to the group's board seen by Reuters on Tuesday.
"Only a much higher price than the current market value of TIM Brasil could adequately compensate the loss of opportunities deriving from such a strategic holding."
Though Fossati's valuation equates to a very high 17 times TIM Brasil's core earnings, research firm Bernstein says that a sale at 7.5 times earnings would clearly create value for Telecom Italia shareholders.
The possibility of a sale was sparked by antitrust issues resulting from Spain's Telefonica raising its indirect stake in Telecom Italia to 15 percent stake.
Both own competing mobile networks in Brazil and the South American country's competition watchdog told Telefonica last month to sell its interest in TIM Brasil or reduce its stake in mobile business Vivo.
Telecom Italia only narrowly fended off an attempt by Fossati to oust the company's board in December, highlighting growing support from institutional investors to his argument that Telefonica has too much sway over the company.
Rebel Telecom Italia investors believe that Telefonica, which has agreed to a gradual takeover of the Italian company, could force its rival into a bad deal in Brazil that favours the Spanish group's own interest in the country.
A sale of TIM Brasil is not part of Telecom Italia CEO Marco Patuano's business plan, though speculation about an imminent offer for the $13.7 billion business has lifted Telecom Italia shares by more than 10 percent this month.
A source familiar with the matter said on Tuesday that talks are under way and an offer for TIM Brasil could be presented if the local competition watchdog signalled it might be feasible.
Patuano has said that only a "convincing" price would persuade him to sell TIM Brasil, which is 67 percent-owned by the Italian group.
Telefonica's goal is to break up TIM Brasil and divide its assets between itself and the other two mobile operators in Brazil, America Movil and Oi, sources familiar with Telefonica's plans have said.
Fossati's letter was accompanied by a study that pegged TIM Brasil's standalone value at 17 billion euros ($23 billion). But after factoring in growth prospects, cost savings and other benefits rivals would reap from a break-up sale, it said that TIM Brasil could be worth as much as 30 billion euros.
The saga is being followed closely by Italian politicians eager to safeguard jobs at one of the country's largest employers.
"I believe TIM Brasil is strategic for Telecom ... We can't accept that it turns into a sort of bad company," Deputy Industry Minister Antonio Catricala said on the Huffington Post's Italian website.
A sale of TIM Brasil would be Telefonica's preferred option to comply with Brazilian antitrust demands because it considers market-leading Vivo as a key asset, sources with direct knowledge of the situation said.
A break-up sale would boost the combined core earnings of TIM Brasil's rivals by more than 2 billion euros, according to Bernstein estimates.
It would also leave Telecom Italia with only its domestic activities, the margins of which have been under constant pressure in recent years because of the economic downturn and fierce competition.
Telecom Italia is due to hold a board meeting on Thursday.