Investigating judges in Lille, in the north of France, are seeking permission from French prosecutors to expand a prostitution probe to include accusations of gang rape in Washington that allegedly occurred in December 2010, the Associated Press reported.
An answer from the prosecutor's office is expected to come next week.
The 63-year-old Strauss-Khan, or DSK as he is also known, is the target of the Lille probe and faces preliminary charges of aggravated pimping.
The Lille probe is investigating whether French officials paid prostitutes with embezzled funds. Prostitution is legal in the country.
The investigation is determining whether Strauss-Kahn was aware of the payments, according to the New York Times.
Two Belgian prostitutes who met with probers claimed DSK was violent during the alleged sexual escapade at the Washington's W Hotel and forced one of the prostitutes to have anal sex without her consent, according to a report by the French newspaper Liberation.
The paper reported one of the prostitutes said Strauss-Khan used force, he held down my hands, he pulled my hair, he hurt me, according to the Associated Press.
A spokeswoman for the prosecutor's office would only say the office is studying the request, to expand the probe, according to Reuters.
There are two possible options: the request is turned down or police open a preliminary investigation, she said.
DSK's lawyers deny the allegations.
Strauss-Kahn absolutely contests having committed the slightest violence of any nature, and notes that the declarations made by the young women are contradictory, DSK attorneys Frederique Beaulieu and Richard Malka said in a statement, according to the AP.
Strauss-Khan has said from the onset that the allegations were part of a plot to undermine his prospects to be France's next president, going so far as to accuse confidants of French President Nicholas Sarkozy as being involved in the conspiracy.
It's unclear whether the group rape ever occurred.
Strauss-Khan was arrested and charged with sexually assaulting Nafissatou Diallo, 33, a Sofitel hotel maid, in one of the posh New York hotel's rooms in May 2011.
But the charges were dropped by New York District Attorney Cyrus Vance in August when Diallo, a native of Guinea living in the Bronx, turned out not to be a credible accuser. She lied about being gang-raped by soldiers in her homeland, amid other falsehoods, The New York Times reported.
However, civil charges filed by Diallo are allowed to proceed. Strauss-Kahn tried to get the case dismissed, citing diplomatic immunity, the AP reported.