As part of a potential deal, Bouygues would receive a 15% stake in Orange valued at €8 billion and the €2 billion in cash, according to French newspaper Le Journal du Dimanche, who reported that the two companies signed the agreement on December 24 2015.
"The teams get along well, the talks are advancing, we'll know quickly whether we can go all the way," according to a source of the paper.
The two companies are expected to meet this week for further negotiations.
An Orange-Bouygues deal would reduce the number of operators in France from four to three, creating a combined entity of approximately 59% of mobile network operator customers.