The Wall Street Journal Journal, citing unnamed sources, said Kenneth Thompson, the lawyer for Sofitel hotel maid Nafissatou Diallo, said he would work to see that the criminal trial foundered in return for a civil settlement.
A similar story in the online Daily Beast news site quoted unnamed sources close to the case saying that settlement talks took place in mid to late June.
The prosecutor's office said it had no comment on the reports. There was no immediate reply to a request for confirmation from lawyers for Diallo and Strauss-Kahn about the claims.
If true, the reports would raise further doubts about Diallo's credibility ahead of a key hearing on Tuesday at which prosecutors are expected to announce whether or not they intend to pursue the case.
The arrest of Strauss-Kahn in May on charges of attempting to rape the housekeeper sent shock waves through France -- where he was a leading politician -- and the International Monetary Fund, from which he soon resigned.
But the prosecution's case has unraveled in recent weeks after the New York District Attorney's office said there were problems with Diallo's credibility, a key factor in a trial where she would be the main prosecution witness.
The Journal reported that prosecutors had requested that Thompson -- who filed a civil suit against Strauss-Kahn on Diallo's behalf last week -- supply them with information about any settlement negotiations.
The newspaper said Thompson denied any claims of settlement talks and quoted him as saying: "We look forward to trying this case before a jury."
Diallo has accused Strauss-Kahn of sexually assaulting her on May 14 in his suite at the Sofitel hotel in Manhattan, and the civil suit filed earlier this month, seeking unspecified damages, accuses him of a pattern of assaulting women in hotel rooms.
Strauss-Kahn has denied the allegations, and his lawyers have said Diallo, a Guinean immigrant, fabricated the claims in order to extract payment.
"We have maintained from the beginning that the motivation of Mr Thompson and his client was to make money," Strauss-Kahn's attorneys said after the civil suit was fired, adding that it had "no merit."
Prosecutors say Diallo lied about being raped in her native Guinea, or changed the story, filed a false tax return and lied on her asylum application. If correct, these revelations would likely give ammunition to Strauss-Kahn's lawyers during cross-examination, when the defense has only to
show reasonable doubt.