MILAN (Reuters) - Egyptian billionaire Naguib Sawiris is ready to invest $1 billion (597 million pounds) to $2 billion (1 billion pounds) in Telecom Italia (>> Telecom Italia SpA) if its biggest shareholder Telefonica (>> Telefonica SA) pulled out from the Italian phone group, according to newspaper Il Sole 24 Ore,.

Sawiris, who unsuccessfully attempted to buy a stake in Telecom Italia in 2012, criticised the presence of the Spanish group because of conflicting interests in Brazil and said Telecom Italia needed cash for investments.

Telefonica, which together with three Italian financial institutions controls 22.4 percent of Telecom Italia through holding Telco, is a direct rival of Telecom Italia in Brazil.

Sources close to Telefonica have said the group would like to break up Telecom Italia's Brazilian unit TIM Brasil (>> TIM Participacoes SA) and share its assets with other telecom companies.

"In the past I made my calculations and put forward a proposal. I think I would reiterate that: I would be ready to invest 1 to 2 billion dollars," Sawiris said when asked how much would he spend on Telecom Italia if Telefonica withdrew from it.

The Brazilian competition watchdog has given Telefonica until mid-2015 to downsize its presence in the south American country, sources close to the matter have said.

If Telefonica fails with its plans over Brazil it might have to consider selling its 15 percent stake in Telecom Italia to comply with Brazilian authority's demands.

"I am waiting until Telefonica makes a decision. I will be patient for a few moths more," Sawiris said.

The Italian partners of Telefonica have signalled they could break up Telco in the coming months and eventually sell their stakes in Telecom Italia, weakening the Spanish group's grip over the Italian group.

Telecom Italia, which is due to appoint a new board next week, is carrying out a 4-billion-euro plan to cut debt and fund investments as it seeks to reverse years of sluggish growth.

(Reporting by Danilo Masoni; editing by Keiron Henderson)