The person spoke to The Associated Press on the condition of anonymity to discuss the private negotiation. The details of the deal were unknown.
Strauss-Kahn lawyer William Taylor wouldn't comment Thursday. Lawyers for the housekeeper didn't immediately respond to phone and email messages.
The person said Bronx Supreme Court Judge Douglas McKeon facilitated the agreement, which hasn't been signed.
The deal would end a legal saga that forced Strauss-Kahn's resignation as head of the IMF and ended his French presidential ambitions last year. Prosecutors dropped related criminal charges.
The housekeeper, Nafissatou Diallo, said Strauss-Kahn attacked her when she arrived to clean his upscale Manhattan hotel suite in May 2011. He said their encounter was consensual and called the lawsuit defamatory.
Strauss-Kahn, 63, initially argued that he had diplomatic immunity from the lawsuit. A judge turned down that claim in May.
The charges halted his political career and seemed to open a floodgate of further sex-crime accusations in France, some going back years, against a man who had been seen as a randy charmer. He has acknowledged some "libertine" behavior but denied doing anything criminal or violent.
The Associated Press generally does not name people who say they have been sexually assaulted unless they come forward publicly, as Diallo has done.
The New York Times first reported the agreement.
In August, a separate case against Strauss-Kahn centered on allegations of rape in a Washington, D.C., hotel was dropped after prosecutors said the accuser, an escort, changed her account to say no rape was involved in the encounter when Strauss-Kahn headed the IMF.