The French Football Federation this evening 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.
"Noel Le Graet, president of the French Football Federation, and Didier Deschamps met in Paris on Saturday," a statement on the FFF's website read.
"They engaged in a discussion on possible terms of contract to be the coach of the France team."
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.
The 43-year-old guided OM to one Ligue 1 title and a record three successive League Cups in as many years on the south coast.
Deschamps, who has also previously managed Juventus and Monaco, endured a difficult campaign last season, however, as OM managed only 10th place in Ligue 1.
Should Deschamps be appointed his first game in charge would be against South American champions Uruguay in Le Havre on August 15.
He could be without a number of his star names before then, however, as the FFF continue to sift through the fall-out of a Euro 2012 campaign that was undermined by off-field problems.
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.
Manchester City midfielder Nasri fell foul of the FFF following his heated argument with a journalist in the wake of Les Bleus' last-eight loss to Spain, while Newcastle forward Ben Arfa was allegedly embroiled in a dressing-room altercation following the 2-0 defeat to Sweden in France's final Group D outing.
Paris St Germain midfielder Menez is to be investigated after allegedly gesturing at goalkeeper Hugo Lloris, while Rennes midfielder M'Vila upset the FFF when he ignored Blanc following his substitution against Spain.
The unsavoury claims have brought back memories of France's disastrous 2010 World Cup, when Les Bleus crashed out at the group stage after the players refused to train following the expulsion of Nicolas Anelka.
On that occasion, Anelka, Patrice Evra, Franck Ribery and Jeremy Toulalan were hit with bans of varying lengths by the FFF.