MILAN- Telecom Italia (TIM) shares rose on Monday as Italy's biggest telecoms company confirmed CVC's interest in taking a stake in its enterprise service arm, while it is also weighing a takeover approach for the group by KKR.

The CVC move comes as newly-appointed TIM Chief Executive Pietro Labriola presses ahead with a plan to split TIM's service business from its network operations as part of a broader strategy to revamp the former phone monopoly.

TIM said CVC proposed setting up an entity including connectivity operations for big corporate clients as well cloud, cybersecurity and IoT services, in which the European private equity firm would take a minority stake, confirming what sources told Reuters on Saturday..

TIM added in statement that its talks with U.S. fund KKR to assess the "attractiveness, actuality and deliverability" of its 10.8 billion euro ($11.9 billion) approach for the group as a whole were ongoing.

Shares in TIM were up 3% on Monday at 0.34 euro after the stock hit a record low of 0.22 earlier this month. The price remains well below the 0.505 euro price at which the KKR approach was pitched late last year.

BOARD MEETING

The TIM board will have a first look at the CVC proposal at a meeting scheduled for Tuesday and also assess the state of play with the KKR approach.

KKR submitted its non-binding takeover proposal for TIM in November, having already invested 1.8 billion euros for a 37.5% stake in the group's last-mile fixed-line network last year.

TIM left the New York-based fund waiting for nearly four months without an answer before agreeing earlier in March to engage in talks, while pressing ahead with its standalone reorganisation to unlock the group "untapped value".

TIM, which is grappling with fierce competition in its domestic market, was hit by multiple downgrades by rating agencies this month after it unveiled a record annual loss and a weak outlook.

Last week KKR said it remained interested in taking over TIM but also wants to discuss the phone group's own plans to combine its fixed line assets with those of state-backed rival Open Fiber.

While TIM's top shareholder Vivendi billed KKR's proposal as too low, state lender CDP is advocating a tie-up of TIM's fixed network assets with those of Open Fiber to avoid a costly duplication of investment to upgrade the national network.

CDP, which owns a 10% holding in TIM, controls a 60% stake in the smaller rival fiber optic firm.

Sources have also said a compromise with KKR could be possible, whereby TIM seeks to deepen existing cooperation with the U.S. fund, involving it in its plans to split off its fixed network infrastructure and merge it with that of Open Fiber.

($1 = 0.9106 euros)

(Reporting by Cristina Carlevaro and Elvira Pollina Writing by Keith Weir editing by Agnieszka Flak)