The Italian group has said it will discuss the possible conversion in the second half of 2015.
Such a move would be designed to generate cash for the heavily indebted company, as savings shares do not have voting rights but are expensive for companies because their holders are entitled to a dividend.
A one-to-one conversion would also require payment from savings share holders, according to the sources.
Telecom Italia has not paid a dividend on its ordinary stock this year but paid 166 million euros on its savings shares.
Two of the sources told Reuters that to make the conversion appealing for both the company and investors, the price gap between the two classes of shares should be at least 20 percent, compared with a current spread of around 15 percent.
A third source said the spread was not wide enough at present, though he expected the conversion to take place early next year.
At 1500 GMT on Wednesday, the ordinary stock traded at 1.106 euros, while the savings shares were worth around 0.9375 euros, a discount reflecting the holder's lack of any say in decisions on the company's future.
The most likely scenario for the conversion would be a voluntary, one-for-one exchange, with the holders of savings shares paying a fee that could be about half the difference in price between the two classes.
Under this scheme, the conversion would generate more than 500 million euros ($565 million) for Telecom Italia, while still allowing holders of savings stock to get ordinary shares at a lower price than if they had to buy them on the market.
Activist investor and fund Amber Capital is a big holder of the savings shares and favours the conversion, according to a source familiar with its strategy.
Filings to the US Securities Exchange Commission Authority last year showed fund manager Massachusetts Financial Services had 5.7 percent of Telecom Italia's savings shares, while investment firm Brandes Investment Partners had 5.8 percent.
A conversion of the savings shares would dilute investors in ordinary stock.
Telecom Italia's top shareholder Vivendi for instance would see its stake fall to 10.7 percent from 15.5 percent unless it buys more shares.