The New York Post cited an unnamed senior investigator as saying prosecutors would drop their charges at a court hearing in two weeks, or even earlier, due to doubts about the credibility of the alleged victim.
In Paris, however, French writer Tristane Banon filed a legal complaint alleging Strauss-Kahn tried to assault her in 2003, when she was 22, her lawyer David Koubbi told Reuters.
Banon, an author and journalist, gave a graphic account in a 2007 TV talk show of her allegation Strauss-Kahn tried to rape her during an interview in a Paris apartment.
This is the first time she has taken legal action.
Her complaint will be examined by a judge who, as a matter of course, would question both Banon and Strauss-Kahn, sending investigators to the United States if necessary, before deciding to either place the Frenchman under investigation or dismiss the case.
In yet another twist to a saga that has captivated much of the world, the hotel maid who accused Strauss-Kahn in May of trying to rape her has sued the New York Post and four of its journalists for reporting that she was a prostitute.
Signs that the US charges are unravelling have set off a round of political sparring that threatens to poison the run-up to an April 2012 presidential election that Strauss-Kahn had been tipped to win for the left.
Strauss-Kahn plans to bring a counter-claim against Banon, his lawyer said on Monday, a routine response in France when a legal complaint is filed against a party who denies misconduct.
The Banon case may fizzle out after a preliminary inquiry unless the judge deems there is tangible evidence of an attempted sexual assault. Given the years that have lapsed since the alleged incident, there could be little aside witnesses' conflicting statements to hold up a court case.
Regardless of the outcome, opinion polls since the weekend suggest that more than half of French voters think Strauss-Kahn's political career is already over.
A judge released Strauss-Kahn from house arrest on Friday, although charges of attempted rape remained in place, after prosecutors said the hotel maid changed details of her story.