The French Football Federation have confirmed that their president Noel Le Graet had met Deschamps to discuss terms of a deal to replace Laurent Blanc.
Blanc stepped down from the helm of Les Bleus last week following the fall-out of their Euro 2012 quarter-final exit to eventual winners Spain.
Deschamps, who captained France to their 1998 World Cup and Euro 2000 triumphs, was quickly installed as favourite to succeed Blanc after he left his post at Marseille by mutual consent last week.
Last week the governing body opened disciplinary proceedings against four members of the squad - Samir Nasri, Hatem Ben Arfa, Jeremy Menez and Yann M'Vila, who are set to be called in front of a disciplinary committee.
Ben Arfa was allegedly embroiled in a dressing-room altercation following the 2-0 defeat to Sweden in France's final Group D outing.