Swisscom is considering a bid for Vodafone's Italian business early next year, after Iliad made a bid for the operator.
A deal would see Swisscom combine Vodafone with its Italian subsidiary, mobile operator Fastweb, reported Bloomberg.
Earlier this week Iliad, which is owned by Xavier Niel, submitted a proposal to Vodafone to merge the two telcos in Italy.
Iliad's offer values Vodafone Italia at €10.45 billion ($11.42bn).
Fastweb has an estimated 3.4 million mobile customers in Italy, while Vodafone has closer to 20 million.
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.