Update: Strauss-Kahn's lawyers in the US said Friday there has been no deal yet.
"The parties have discussed a resolution but there has been no settlement. Mr Strauss-Kahn will continue to defend the charges if no resolution can be reached," attorneys William Taylor and Amit Mehta said in a statement.
“Dominique Strauss-Kahn, who himself has been to New York several time in recent months, has confided to several of his friends that the main elements of an agreement had been reached at the end of the summer,” the paper reported in its edition appearing Friday afternoon.
“According to his confidences, he had to pay six million dollars (4.64 million euros) to the woman who accuses him of sexual assault,” the paper said.
Strauss-Kahn’s lawyers “vigorously” denied the report, calling it “far-fetched and erroneous”, adding that neither they nor their client would comment on the case.
Le Monde says that Strauss-Kahn will pay the settlement by borrowing half from his bank and half from his wife, Anne Sinclair, from whom he separated last spring.
The judge in charge of the case, Douglas McKeon, has refused to comment on a settlement but said that the court hold a session next week.
Lawyers for both parties have been meeting almost weekly since McKeon refused to dismiss the case in May, according to the Wall Street Journal.
Before the case hit the headlines, Strauss-Kahn was widely tipped to be the French Socialist Party’s candidate against Nicolas Sarkozy in this year’s presidential election.
The party’s national secretary Harlem Désir welcomed the news, while regretting that “the complete truth has not been revealed”.
He described speculation that Strauss-Kahn may stand in local elections in Sarcelles, where he used to be mayor, as “rumours”.
A French court this week put off a decision on whether to pursue a case of pimping against him until 19 December.