MILAN (Reuters) - Poste Italiane has agreed broad terms with Vivendi to buy the bulk of the French group's stake in Telecom Italia and become its main investor, three sources close to the matter said on Saturday.

State-controlled Poste, whose businesses include energy, payments and phone services as well as mail and parcels, became an investor in TIM in February with a 9.8% stake, replacing state lender CDP.

The sources said it had now reached a broad agreement with Vivendi to buy most of the French group's 18.4% stake in TIM.

They did not disclose the exact stake or price, but two said Poste would remain below the 25% threshold above which, under Italian law, it would have to make an offer for the rest of TIM.

Though nothing has been signed, a deal is close to being finalised and an announcement expected soon, the two sources said.

Vivendi and Poste declined to comment.

TIM is Italy's former phone monopoly and a business of strategic national importance.

After spinning off its fixed-line grid last year, TIM could now become involved in the consolidation expected in a sector where profit margins are seen as too thin to finance the required investments.

When it first invested in TIM, Poste said it was ready to support it as the industry consolidates.

For Rome to preserve a meaningful presence in TIM if it ties up with another telecoms firm, Poste first needs to boost its stake.

Reuters was first to report that Poste was ready to increase its holding. Sources said earlier this week that Poste was in talks with Vivendi, which recently cut its stake in TIM to 18.4% from 23.9%.

A senior Treasury official also said this week that Poste had "the right credentials" to be a leading investor in TIM because it could be both a financial and an industrial partner.

(Additional reporting and writing by Valentina Za.; Editing by Mark Potter)