Metroweb's state owner rejects Telecom Italia proposal - sources

* Telecom proposed full ownership of Metroweb in 5 years

* Rejection could favour Vodafone in talks for stake

* Battle comes as Italian govt pushes for digital plan (Adds details, context)

By Danilo Masoni and Alberto Sisto

MILAN/ROME, April 23 (Reuters) - The state owner of Italy's Metroweb has rejected a proposal by Telecom Italia (Other OTC: TIAJF - news) to take a stake in the broadband company and gradually reach full ownership, according to two people close to the matter and an email seen by Reuters.

The latest twist in long-running talks between Telecom Italia and state lender Cassa Depositi e Presititi (CDP) could favour Vodafone, which has also set its sight on the broadband firm.

The battle for Metroweb, controlled by infrastructure fund F2i and CDP through its investment arm Fondo Strategico Italiano (FSI), is politically sensitive because Prime Minister Matteo Renzi considers it a building block for a 12 billion euro ($13 billion) plan to roll out faster networks.

"CDP and FSI are not in the condition to go ahead ... at terms outlined in the MOU (memorandum of understanding) draft sent by Telecom Italia," FSI head Maurizio Tamagnini told Telecom Italia CEO Marco Patuano in an April 21 email seen by Reuters and leaked to Italian newspapers.

It was not clear whether the rejection puts an end to negotiations between Telecom Italia and CDP.

Under its proposal, Telecom Italia would initially take a 40 percent voting stake in Metroweb and bring it to 100 percent over five years as it carries out investments to bring fibre cables close to the homes in 250 cities, one source said.

Talks with Telecom Italia over Metroweb had already hit a stumbling block earlier this year due to disagreements over the ownership structure of a deal, and the phone company's chairman, Giuseppe Recchi, said in February the board had concluded that conditions were not yet right for an agreement.

Metroweb is 53.8 percent owned by F2i and 46.2 percent by CDP unit FSI. CDP also owns a stake in F2i.

Rivals Telecom Italia and Vodafone have set their sights on the company as they seek to meet growing consumer demand for bandwidth-consuming services.

CDP has said that Telecom Italia could buy a majority stake in Metroweb but it would rather have other phone operators, such as Vodafone, also as shareholders.

The presence of other operators is something Telecom Italia is not willing to accept. (Additional reporting by Luca Trogni; Editing by Pravin Char)