Sources say that Bouygues will sell mobile spectrum and mobile antennas to address regulators' concerns that the acquisition would create a dominant player in the country.
A rival bid has also been reportedly prepared by cable operator Numericable, owned by billionaire Patrick Drahi, for approximately €14.75 billion ($20.25 billion).
Earlier last year, French telco Vivendi had planned to demerge SFR as the company looked for ways to reduce debt.
SFR and Bouygues signed a deal in January this year to share their mobile networks, in an effort to reduce costs for both companies.