The French Football Federation are giving the former Olympique de Marseille boss as much time as is necessary to decide if he will take charge of his country
The 43-year-old was immediately installed as the clear favourite to replace Laurent Blanc, who recently left his position as Les Bleus' coach, following the side's Euro 2012 quarter-final exit.
However, it was soon reported that the French Football Federation (FFF) was knocked back in its attempts to appoint Deschamps, a rumour that was quickly denied by president Noel Le Graet.
The governing body is reportedly willing to let the World Cup-winning captain take as long he wants to weigh up his options, but it is believed he will make up his mind before the end of the week.
Other names linked to the role include Arsenal manager Arsene Wenger and France legend and current Real Madrid director Zinedine Zidane.
Deschamps enjoyed success at Olympique de Marseille, winning the Ligue 1 title in 2010 but left at the end of the past season after a campaign of underachievement, despite a Coupe de la Ligue triumph.