According to a local website, both companies had discussed a possible merger with French competition authorities.
SFR, Vivendi’s largest subsidiary, is reportedly suffering from the arrival of low cost operator Free, which launched services last January.
Vivendi has been seeking to cut its debt and improve its flagging share price in the past few months, and it has already put its units in non-core markets in Brazil and Morocco up for sale.
According to Reuters, the company’s chief executive has said the future of SFR will largely depend on whether regulators will approve network sharing agreements and mergers.
All parties were not available for comment at this stage.