By Elvira Pollina, Valentina Za and Giuseppe Fonte

MILAN (Reuters) - Poste Italiane is considering a potential investment in Telecom Italia (TIM), two people with knowledge of the matter said, as the former phone monopoly also draws interest from rival Iliad and private equity fund CVC Capital Partners.

Stiff price competition has long been eroding operators' profit margins in Italian telecoms and curbing their ability to make necessary investment, hence the need for consolidation.

Sources told Reuters on Friday that low-cost French telecoms group Iliad and CVC had separately informed the Italian government of their respective interest in potential TIM deals.

State-backed Poste, which offers mobile phone services through Poste Mobile, is also evaluating whether any potential commercial partnership could be strengthened through an equity investment.

No decision has yet been taken, the sources said, and TIM does not feature on the official agenda of a board meeting Poste had scheduled for Monday, one of them added. However, a second person said it could be discussed on Monday.

Italy includes TIM among corporate assets that are strategic for the country, and state-investor Cassa Depositi e Prestiti (CDP) owns a 9.8% stake in TIM.

One possible way for Poste to invest in TIM would be to take CDP's stake, the two people said. 

CDP, which is TIM's second biggest investor after French media group Vivendi, declined to comment. Vivendi is also open to divesting its 24% TIM stake, sources have previously told Reuters.

Poste would be a state-backed investor like CDP, but it would have the advantage of running a business that lends itself to commercial partnerships with TIM.

At current market prices, CDP's stake in TIM is worth more than 450 million euros ($464 million). TIM shares traded above current levels when CDP invested in the group in 2018-2019, which exposes it to a capital loss in a potential disposal.

NEXI SWAP?

Under one possible scheme being examined, in offloading its TIM stake to Poste, CDP could take Poste's 3.78% stake in Nexi, which is worth around 210 million euros at current prices, one of the first two sources and a third source said.

CDP, Nexi and Poste all declined to comment.

Poste has been growing its own payments division, which has come to provide a significant contribution to earnings. CDP already has 14.5% of Nexi.

Europe's payments sector is seen in need of consolidation and a combination between Nexi and French rival Worldline has long appeared an obvious option, to counter the growing dominance of U.S. players.

A bigger CDP stake in Nexi would strengthen Italy's position vis-à-vis France, which is a shareholder in Worldline, if the two were ever to explore a tie-up, bankers have said.

TIM shares, which gained 6.3% on Friday, stood 0.8% higher by 1122 GMT on Monday at 0.302 euros.

TIM is due to present a strategy update on Thursday after CEO Pietro Labriola last year sold the group's main asset, its landline grid, in a multi-billion deal with U.S. fund KKR.($1 = 0.9697 euros)

(Reporting by Elvira Pollina, Valentina Za and Giuseppe Fonte, editing by Giulia Segreti and Keith Weir)