Strauss-Kahn, who returned to Paris after New York rape charges against him were dropped, wanted the interview about the alleged assault on Tristane Banon conducted as soon as possible, lawyers Frederique Baulieu and Henri Leclerc said.
(Read: "Strauss-Kahn acquitted of sex crimes")
Strauss-Kahn, who has complained of media intrusion since returning to Paris on September 4, spent around three hours at the Paris police station, a source close to the inquiry said.
Banon came forward with her allegation in June after Strauss-Kahn was arrested in New York and accused of attempted rape by a hotel maid there.
The French writer, now 32, says that Strauss-Kahn, who had a reputation as a womaniser even before he was accused of sexual assault in New York, tried to rape her in an empty Paris apartment in 2003.
He had to be interviewed for the inquiry to wind up, and friends of the former IMF chief have said he wanted to be heard as soon as possible "to draw a line under this matter."
Strauss-Kahn has denied both claims. The New York prosecutor's case fall apart when it emerged that his accuser there had a history of dishonesty.
The French justice system has already interviewed several people, including prominent politicians, as part of the inquiry into the 2003 alleged attack, including former Socialist party leader Francois Hollande.
Banon's mother is herself a Socialist politician.
Strauss-Kahn arrived back in Paris to a media frenzy eight days ago, a fortnight after the New York charges were dropped. His friends have said he will speak publicly "in the fortnight" following his return.
The 62-year-old Socialist politician, whose hopes for the French presidency have been torpedoed, still faces a civil suit from his New York accuser as well as the Banon claims.
Strauss-Kahn has filed a defamation suit against the writer.
After completing a preliminary inquiry, the French prosecutor can decide whether there is a case for prosecution, that there is no case, or that the alleged crime has been prescribed because it happened so long ago.
Those close to the inquiry say that the lack of material evidence eight years after the alleged crime is complicating a potential case.
Banon on Saturday lamented what she said was the "hero's welcome" given to Strauss-Kahn on his return to France.
"I hear people telling me of their disgust, I need their support to remain upright, yet I am the one who bows my head and stays out of sight while others laugh at the cameras," the writer said in a message sent to AFP and other media and posted on her Facebook page.
Calling for a picket in Paris on September 24, Banon wrote: "There is a real problem in this country, things must change.
"Rape and violence against women cannot be trivialised, money and power cannot place someone be above the law."
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its amazing how the US legal system was quick to negate all claims of alleged rape, just because the lady had lied on some of her immigration documentation....despite the fact that DSK has a problem keeping his pants on, and the french insist they don't take such acts lightly...but the allegations remained uninvestigated and that just makes DSK stronger!