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The two companies have contacted French competition authorities about a possible merger between Iliad's low-cost mobile operator Free and Vivendi's SFR, BFM said.
SFR, Vivendi's biggest unit, is suffering from the arrival of Free in the market last January.
Entertainment-to-media conglomerate Vivendi began a strategy review in May to boost its flagging share price and cut debt, and has put units in Brazil and Morocco up for sale.
Its chief executive said last month the future of SFR would depend, in part, on whether regulators approved network-sharing deals or mergers.
BFM also reported that industrialist Vincent Bollore, who was given a seat on Vivendi's board in December, would be opposed to an eventual merger between SFR and French cable operator Numericable.
Iliad, Vivendi and France's Autorite de la Concurrence were not available for comment.
Reporting by Elena Berton and Matthieu Protard; Editing by Dan Lalor