The 43-year-old resigned as Marseille boss on Monday but it was previously claimed that he had turned down the chance to take charge of the Euro 2012 quarter-finalists
It was initially claimed that the former Bleus midfielder, who stepped down as Marseille boss on Monday, was not interested in the position.
However, Deschamps has been persuaded to accept the job by his family, who do not want to leave France, according to RTL.
RMC had reported that the 43-year-old coach rejected the opportunity to take the reins because he was unhappy with the way in which Blanc's departure had been handled.
However, FFF president Noel Le Graet promptly dismissed the veracity of the story and insisted that Deschamps had not ruled himself out of the running.
It now seems as if Deschamps, who has also previously coached Monaco and Juventus, is now set to succeed his former international team-mate at the helm, with RTL reporting that his appointment could be confirmed as early as Saturday.