Bouygues said in a separate statement that its board would meet on Tuesday to discuss what it called Altice's "unsolicited offer", adding that no negotiations between the two sides were underway.
Telecoms tycoon Patrick Drahi, the controlling shareholder of Altice, submitted a bid for Bouygues Telecom in recent weeks worth around 10 billion euros ($11.4 billion) in cash, sources told Reuters on Sunday.
In a separate statement, Numericable-SFR and low-cost operator Iliad said that they were in exclusive talks over selling a portfolio of Bouygues assets to Iliad if the first deal went through.
Iliad would take over much of Bouygues Telecom's mobile towers and spectrum, in an effort to calm competition regulators' concerns about the French mobile market going from four to three players if Bouygues is swallowed by Altice, two sources said on Sunday.
"Altice will update the market in due course," said the statement.