Iliad Group has submitted a proposal to Vodafone to merge the two telcos in Italy.
Iliad, which is owned by French tycoon Xavier Niel, values Vodafone Italia at €10.45 billion ($11.42bn) in its offer.
Iliad will receive €500 million ($546m) in cash and 50 percent of the new business as part of the proposal.
While Iliad would make €500 million ($546m) in cash and 50 percent of the new business.
The offer would allow Iliad the option to purchase an additional 10 percent of the merger company's shares every year, paving the way towards full control.
It was reported earlier this year that Iliad had revived merger talks with Vodafone, after previously failing to do so with an €11.25 billion ($12.3bn) consortium bid for the unit last year.
In September of last year, Niel acquired a 2.5 percent stake in Vodafone Group through his investment vehicle Atlas Investissement.
Vodafone acknowledged the proposal for a merger in a statement.
"Consistent with its previous statements, Vodafone is supportive of in-market consolidation in countries where it is not achieving appropriate returns on invested capital and confirms it is exploring options with several parties to achieve this in Italy, including through a merger or a disposal," said Vodafone.
"There can be no certainty that any transaction will ultimately be agreed. If required, a further announcement will be made when appropriate."
Iliad only entered the Italian market back in 2018, as a low-cost challenger brand. The operator currently has a market share of around 9.2 percent.
Meanwhile, Vodafone's share is estimated to be 27.4 percent, just behind Telecom Italia (TIM), with 28 percent.
Vodafone has shown a desire to consolidate its business across a number of markets in recent years.
In the UK, the company is poised to merge with Three to become the UK's biggest telco in a £15bn ($19bn) deal.
Vodafone Group chief executive Margherita Della Valle has previously hinted at plans to "simplify the business."
In October the company confirmed it has agreed to sell its Spanish business to UK investment firm Zegona for $5.3 billion.
Vodafone has previously exited the Hungarian market, and finalized an exit from Ghana this year, selling a majority stake to Telecel Group.
