MILAN, Dec 21 (Reuters) - Telecom Italia's board will meet on Sunday afternoon to discuss a long-awaited plan to convert its savings shares into ordinary stock, two sources said, a move aimed at cutting costs and simplifying its capital structure.

The special board meeting comes a day after the former phone monopoly won a 1-billion-euro ($1.2-billion) payout from the government in a long-running lawsuit, providing fresh resources to fund its savings-share conversion plan and help it resume dividend payments, which it halted in 2022.

The board will discuss the final terms of the conversion plan and is expected to call a shareholder meeting at the end of January to vote on the proposal, the two sources with knowledge of the matter told Reuters. 

The board is also expected to name a director to fill a vacant seat, the sources added, without going into further detail.

A Telecom Italia spokesperson declined to comment.

The conversion of savings shares would mark another key step in the company's restructuring, following the 19.8-billion-euro sale of its fixed-line network to KKR aimed at cutting debt, and the entry of state-backed Poste Italiane as its largest shareholder.

Nearly 28% of Telecom Italia's capital structure consists of savings shares, which carry a guaranteed minimum dividend of about 166 million euros a year.

Chief Executive Pietro Labriola has repeatedly said Italy's biggest phone group aims to eliminate its dual-class share structure and shed costly savings shares in a market-friendly way.

At Friday's market close, the savings shares traded at 0.57 euros each, offering a premium of 7 cents over the ordinary stock.

The conversion would need a two-thirds majority at the meeting of ordinary shareholders, and would dilute the holdings of existing ordinary investors, including top shareholder Poste Italiane, which has a 27.3% stake. 

Savings shareholders will also vote upon the proposal separately. 

Telecom Italia sought to eliminate its savings shares a decade ago, but the plan was blocked by then top investor Vivendi.

($1 = 0.8541 euros)

(Reporting by Elvira Pollina, editing by Andrew Heavens)

By Elvira Pollina