* Telecom Italia seen in play before year out - Bernstein
* Carlos Slim could be eyeing firm's Brazil unit - analyst
* Telecom's controlling shareholder pact under discussion
* Shares rise as much as 10 percent to one month high (Adds more analyst comment, background, shares)
By Stephen Jewkes
MILAN, Aug 30 Telecom Italia SpA shares jumped as much as 10 percent on Friday, on speculation it might be the next quarry in a recent upsurge in dealmaking in Europe's telecoms industry.
Analysts at brokerage Bernstein said a lowly valuation, an attractive business in Brazil and a willingness among some Telecom Italia shareholders to sell could make the company a takeover target before the year is out.
They tipped Vodafone, Telefonica Softbank , and AT&T - possibly in combination with Mexican billionaire Carlos Slim's America Movil - as potential bidders and said the shares could double from current levels.
At 1330 GMT, Telecom Italia shares were up 9.6 percent at 0.4176 euros, the biggest rise by a European blue-chip stock , after touching a one-month high of 0.4218 euros.
The company was not immediately available to comment on the speculation.
The telecoms sector has seen a surge in dealmaking as companies look to take advantage of low interest rates, and as European players battle to cope in a saturated market with recession-hit consumers and expensive network upgrades.
U.S. group Verizon Communications Inc is close to buying an outstanding stake in Verizon Wireless from Vodafone Group Plc for potentially $130 billion, sources close to the matter have said, while a report said AT&T would examine Vodafone's remaining assets.
Spain's Telefonica has agreed a deal to buy German mobile operator E-Plus from KPN, while Carlos Slim's America Movil (AMX) threatened on Friday to abandon a plan to buy the rest of KPN after the Dutch group's foundation said it might block a deal.
A Milan-based broker said Slim's next port of call could be Brazil, via Telecom Italia.
"We believe that America Movil could well make Telecom Italia an offer they can't refuse for (its Brazilian asset) TIM Brazil," said the broker, who asked not to be named.
Shares in debt-laden Telecom Italia have been languishing near historic lows due to falling margins in Italy and a slowdown in Brazil, its other main market.
"Telecom Italia is the cheapest of stocks we cover, trading at just 4.0 times EBITDA (earnings before interest, tax, depreciation and amortisation), a 22 percent discount to incumbent peers," the Bernstein analysts said, referring to other firms with leading positions in their home markets.
They said the Italian government in theory viewed Telecom Italia as a strategic asset, but might be willing to accept certain foreign bidders.
Prime Minister Enrico Letta said earlier this month there were no plans for state holding CDP to invest in Telecom Italia.
"We think Vodafone, Telefonica, AT&T/AMX and Softbank would probably all be welcome in roughly that order," Bernstein said, adding that Telefonica - the biggest stakeholder in Telecom Italia's core investor group Telco - and a combination of AT&T and America Movil (AMX) were the most likely suitors.
Telco's investors - Telefonica, Mediobanca, Generali and Intesa Sanpaolo - have until the end of September to say if they want to exit the vehicle.
Mediobanca has already said it plans to leave while Generali has said it would eventually do the same but when conditions were right.
Telecom Italia was involved in abortive talks earlier this year with Hong Kong's Hutchison Whampoa over a possible tie-up.
Last year, Telco shareholders turned down an offer by Egyptian tycoon Naguib Sawiris to inject 3 billion euros of cash into the debt-laden Italian telecoms company. (Editing by David Cowell and Mark Potter)