Strauss-Kahn, 62, a steward of the world economy and a leading candidate for the French presidency when he was arrested on May 14, may now be released on his own recognizance and freed from house arrest as soon as Friday, the paper said.
A source familiar with the case said on Thursday that the credibility of the maid who accused him has come into question.
"The credibility is in question," the source, speaking on condition of anonymity, told Reuters.
The New York Times said prosecutors had met with Strauss-Kahn's lawyers on Thursday and the parties were discussing whether to dismiss the felony charges.
Strauss-Kahn's defense attorney, Benjamin Brafman, said earlier on Thursday that their client would go back to court in New York on Friday at 11:30 a.m. (1530 GMT, 7.30 pm UAE time) before Judge Michael Obus to seek changes to his bail conditions.
"Indeed, Mr. Strauss-Kahn could be released on his own recognizance, and freed from house arrest, reflecting the likelihood that the serious criminal charges against him will not be sustained," the paper said. "The district attorney's office may try to require Mr. Strauss-Kahn to plead guilty to a misdemeanor, but his lawyers are likely to contest such a move."
Strauss-Kahn resigned from the IMF on May 19 and pleaded not guilty on June 6, vehemently denying the allegations. He faced up to 25 years in prison if convicted.
LIES AND INCONSISTENCIES
The New York Times quoted what it said were two well-placed law enforcement officials as saying that although forensic evidence showed there had been a sexual encounter between the French politician and the maid, the accuser had repeatedly lied.
It said that prosecutors had discovered issues involving the asylum application of the 32-year-old housekeeper, who is Guinean, and possible links to criminal activities, including drug dealing and money laundering.
The paper added that prosecutors' investigators had discovered that the woman had had a phone conversation with an incarcerated man within a day of her encounter with Strauss-Kahn in which she discussed the possible benefits of pursuing the charges against him. The conversation was recorded.
It added that the man, who had been arrested on charges of possessing 400 pounds (180 kg) of marijuana, was among a number of individuals who had made multiple cash deposits, totaling around $100,000, into the woman's bank account over the last two years.
From the start, the case hinged on the purported victim, a Guinean immigrant and hotel maid, 32, who cleaned the $3,000-a-night suite at the Sofitel hotel where Strauss-Kahn paid $800.
Prosecutors presented her case before a grand jury, confident in the women's story that Strauss-Kahn sprang naked from the bathroom, chased her down and hall and tried to force her to perform oral sex on him. He was indicted.
Now "prosecutors do not believe much of what the accuser has told them about the circumstances or about herself," the Times reported.
With his resignation, Strauss-Kahn severed all his ties to the IMF. Christine Lagarde, who just stepped down as French finance minister, takes over the top IMF job on Tuesday.
Pulled from the first-class section of a flight to France, Strauss-Kahn was arrested and displayed before cameras in a "perp walk" that some French found slightly barbaric and prejudicial against his defense and standing in French politics.
A grand jury indicted him, and after a few nights in New York's notorious Rikers Island jail, he was eventually relocated in the swanky Tribeca neighborhood under house arrest.
Such a narrative could play well in France, where commentators immediately suggest that Strauss-Kahn, known as the "great seducer" of French politics for his charm and appetite for women, could have been set up by political opponents.
After the circus-like events of his arrest, Strauss-Khan was released on $1 million cash bail and a $5 million bond, and is under house arrest in a townhouse in the Tribeca neighborhood of Manhattan, where he is equipped with an electronic monitoring device and under the 24-hour watch of armed guards. The arrangements are costing Strauss-Kahn $250,000 a month.