Radio France Internationale reported that Lagarde is expected to be charged with fraud and with embezzlement of funds for her role in a legal case involving Bernard Tapie, a businessman and politician.
She also could be called to court as a witness and not charged, Radio France Internationale reported Wednesday.
The newspaper Le Monde reported that the charges, if filed, will claim that Lagarde helped settle a legal matter that concluded with an award of $521 million for Tapie and that her intervention was a payoff for his support of former French President Nicolas Sarkozy.
Tapie, in turn, has accused the French government, now headed by Socialist President Francois Holland, of manipulating the legal system to fabricate charges against Lagarde, who was the French finance minister during the period in question.
Lagarde is expected to appear before a magistrate Thursday or Friday, Radio France Internationale reported.
She is not expected to resign from the International Monetary Fund due to the charges, which she is expected to dispute. But the IMF has inserted a clause in her contract that instructs Lagarde to "strive to avoid even the appearance of impropriety in your conduct."
The phrase was inserted into the IMF director's contract after Lagarde's predecessor at the IMF, Dominique Strauss-Kahn, resigned to devote time to defending himself from charges of sexually assaulting a maid in a New York hotel.