"Renewed preliminary discussions" are taking place, Orange said, adding that both groups have signed a confidentiality agreement.
"For the moment, no decisions have been taken and there is no guarantee that there will be an outcome to these preliminary discussions," Bouygues said.
The statements confirmed reports in the press over the last few weeks that the two were talking.
Orange is France's leading mobile phone and cable operator, while Bouygues Telecom is its third.
A tie-up would reduce the number of operators in France to three, so it would have to be approved either by France's competition watchdog or the European Union's, since Orange has widespread interests outside France.
The other operators, Free and SFR-Numericable, would have to be invited to take part in negotiations and could buy parts of Bouygues' business.
Orange, of which the French state owns a majority 23 per cent share, will be under government pressure to preserve jobs.
Bouygues wants to keep an interest in telecoms with two seats on Orange's board, one of them for Martin Bouygues, and 15 per cent of Orange's capital, second to the state whose share would be reduced to 19 per cent, according to the Journal du Dimanche newspaper.
Both sides have agreed to put Bouygues Telecom's value at 10 billion euros, the same amount that Altice boss Patrice Drahi offered last June, the paper reports.