Star player Thierry Henry has also asked for an interview with France's President Nicolas Sarkozy.
Bachelot says she feels it is ‘inevitable' that Jean-Pierre Escalettes will have to relinquish his post as head of the French Football Federation.
Although Bachelot does not have ministerial power to dismiss FFF president Escalettes following Les Bleus' woeful World Cup campaign - and she claimed that is not a course of action she would take even if she did - she hinted his position would become untenable.
Bachelot said: "The departure of Jean-Pierre Escalettes is not something I want but I find it inevitable."
France's efforts in South Africa were blighted by team infighting which culminated in the exclusion of Nicolas Anelka, a decision which then led to the rest of the squad boycotting a training session.
The repercussions have already been felt and Bachelot thinks Escalettes will also be a casualty.
She added on RTL radio: "The players have not received any remuneration, the coach is going so the last part of this disaster is the federation."
Escalettes, however, has no plans to walk away. The 75-year-old, when asked if he intended to quit, said "it was not in his nature".
Dissecting the reasons behind their World Cup failure has dominated the sporting agenda in France ever since the whistle blew on their final game against South Africa on Tuesday.
President Nicolas Sarkozy has become involved and is scheduled to meet veteran striker Thierry Henry - a hugely influential figure within the France camp - today.
The presidential palace confirmed the Barcelona star had called Sarkozy to request a meeting upon the team's return from South Africa.
"Henry called the president from South Africa to tell him that he wanted to see him on his return," a statement from the presidential palace, L'Elysee, read.
France finished bottom of Group A with only one point from their three games.