The Wall Street Journal cited officials familiar with the case who said prosecutors seem to be on the verge of dismissing the charges altogether, as doubts increased about the woman's reliability as a witness.
"It would have to be that I believed every word that came out of her mouth, and that I believe in the criminal aspect of what occurred," said Assistant District Attorney Joan Illuzzi-Orbon, discussing considerations she will weigh in deciding whether or not to proceed with the case.
The New York Post meanwhile quoted a top investigator as being even more emphatic that a dismissal is likely, saying: "We all know this case is not sustainable."
The source told the daily that dismissal of the charges is "a certainty," and likely will happen at Strauss-Kahn's next scheduled court date July 18.
"Her credibility is so bad now, we know we cannot sustain a case with her," the source told The Post, referring to the Guinea-born hotel maid who accused the Frenchman of attempting to rape her when she came to clean his luxury suite on May 14.
The paper cited defense sources as describing a different scenario, whereby Strauss-Kahn engaged in consensual sex with the maid but then angered her by refusing to pay for it, prompting her accusations.
The sexual assault charges drove Strauss-Kahn to resign as head of the International Monetary Fund (IMF) and initially appeared to have dashed the political career of the man once seen as a likely future French president.
But on Friday Strauss-Kahn was released from house arrest after prosecutors said the maid had lied to a grand jury, raising the possibility that the case could be thrown out because of its key witness's lack of credibility.
Strauss-Kahn has denied all charges against him.
Meanwhile, The New York Times reported Tuesday that a rape counselor for St. Luke's-Roosevelt Hospital Center offered a graphic and detailed written account of the alleged sexual assault.
The report suggested a serious sexual attack, but also underscored inconsistencies that have seriously undermined the woman's credibility.
The rape counselor described an assault in which the woman says her attacker put his hands under her clothes and touched her crotch area, the report said.
The housekeeper said Strauss-Kahn grabbed her by the hair and forced her to perform oral sex, while her attorney Kenneth Thompson had said the housekeeper suffered bruising to her genitals during the episode.
While prosecutors still believe there is evidence of a forcible sexual attack, they admitted in a letter to the defense that the woman lied on her asylum application and tax returns.
And law enforcement officials told The Times there were suspicious deposits made to a bank account in her name and a phone call she placed to a man in federal prison in Arizona in which she discussed Strauss-Kahn.
There also have been discrepancies related to her whereabouts in the immediate aftermath of the alleged assault.
The daily wrote that the housekeeper told investigators that she fled the room after the alleged attack.
But her statements to the rape counselor were that she watched him get dressed afterward, suggesting that she indicated she was still in the room, at least briefly, after the incident.
That scenario appears to contradict what prosecutors said she described in grand jury testimony, in which she said she waited in the hallway for Strauss-Kahn to leave the suite following the alleged attack.
Prosecutors told the Times they responded appropriately, given the evidence they had.
"We're doing our job," Illuzzi-Orbon told the Times. "We don't get paid by indictment. We don't get paid by convictions. We get paid to do the right thing."