"Laurent Blanc has contacted the FFF president, Noel Le Graet, to tell him his decision not to ask for another contract," the FFF said in a statement on their website.
France lost 2-0 to holders Spain in the quarter-finals of Euro 2012 last Saturday.
Deschamps, Blanc's team-mate and captain in the France squad that won the 1998 World Cup and Euro 2000 titles, is the front runner to take over amid speculation that he is close to leaving Olympique Marseille, who he has coached since 2009.
The French federation's executive committee is due to meet on Tuesday when a replacement for Blanc will be discussed.
"If Laurent Blanc leaves it's a shame because he had indicated his wish to continue. But Didier Deschamps is among the very good coaches," former France captain and current UEFA president Michel Platini was quoted as saying in French media on Saturday.
"It is the FFF president who chooses. I do not think we have bad players. Progress has been made, we have potential but it is our [rightful] place [to have been] in the quarter-finals. Anyway, Didier Deschamps does know the team."
