LILLE, France, May 4 (Reuters) - French investigators looking into Dominique Strauss-Kahn's ties to a suspected prostitution ring in the northern city of Lille want to extend the inquiry to cover alleged group rape by the former IMF chief and three friends, prosecutors said on Friday.

Strauss-Kahn is under formal investigation over whether he was aware he was dealing with prostitutes and pimps when attending sex parties in Lille, Paris and Washington in 2010 and 2011 allegedly organised by business acquaintances.

Investigators have asked prosecutors to widen the inquiry after a prostitute told them in her deposition that Strauss-Kahn and friends forced her to have sex in a group when she came to Washington to meet him in December 2010.

The woman has not filed a formal complaint.

"The prosecution is studying the request," a spokeswoman for the prosecutors said. "There are two possible options: the request is turned down or police open a preliminary investigation."

Strauss-Kahn's lawyer Henri Leclerc declined to comment on the new allegation. In March Leclerc vowed to challenge the existing inquiry and said the former finance minister was being hounded for his "libertine ways".

In a scandal that dashed his ambition to run for French president, Strauss-Kahn was arrested in New York last May on charges, later dropped, of trying to rape a hotel maid.

He quit his post as International Monetary Fund chief as he was briefly held in New York's Rikers Island prison.

After criminal charges were dropped over concerns about the maid's credibility, Nafissatou Diallo pressed ahead with a civil case. A New York judge this week rejected Strauss-Kahn's claim of diplomatic immunity, meaning the case can move forward.

Strauss-Kahn's fall from grace saw Francois Hollande emerge as the Socialist candidate for the French presidential election and opinion polls give him a six-point lead on average against incumbent Nicolas Sarkozy for Sunday's runoff vote.

Strauss-Kahn, a former high-flyer on the international scene, has kept a low public profile through the campaign and was shunned by several Socialist heavyweights who walked out of a lawmaker's birthday party last weekend when they discovered he was attending.

His name came up during an election debate on Wednesday, with Sarkozy saying he would not take morality lessons from politicians who had considered him as a possible candidate and Hollande retorting that it was Sarkozy who nominated him as IMF head.

Strauss-Kahn was placed under formal investigation in March in the Lille case which had already led to the arrest of eight people, including two Lille businessmen and a police commissioner. (Reporting by Pierre Savary in Lille and Thierry Leveque in Paris; Writing by Leigh Thomas; Editing by Catherine Bremer and Myra MacDonald)

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  • May 13

    Strauss-Kahn checks into the Sofitel Hotel near Times Square in New York City.

  • May 14

    A 32-year-old hotel maid contacts police, claiming that Strauss-Kahn emerged nude from the bathroom in his $3,000-a-night suite and sexually assaulted her. Strauss-Kahn is arrested at John F. Kennedy Airport where he had boarded a Paris-bound flight.

  • May 16

    After appearing in court where he is formally charged, Strauss-Kahn is sent to New York's Rikers Island instead of being granted bail. He is placed on suicide watch while at Rikers.

  • May 18

    Strauss-Kahn <a href="http://www.guardian.co.uk/world/2011/jul/01/timeline-strauss-kahn-case" target="_hplink">formally resigns</a> as managing director of the IMF and denies all the allegations. He is formally indicted by the grand jury and the seven charges against him are confirmed. He faces a potential maximum of 74 years prison if convicted.

  • May 20

    Strauss-Kahn is released from Rikers and moves into a temporary apartment near Wall Street, where he must submit to round-the-clock surveillance under house arrest. He later moves to a Tribeca townhouse rented for a reported $50,000 a month.

  • May 27

    Just days after media reports suggest that that traces of Strauss-Kahn's semen have been found on the maid's shirt, French President Nicolas Sarkozy calls the case a "sad" affair.

  • June 7

    The former head of the IMF <a href="http://www.guardian.co.uk/world/2011/jun/07/dominique-strauss-kahn-denies-attempted-rape" target="_hplink">pleads</a> not guilty to allegations of attempted rape and the sexual assault of a hotel maid. Hundreds of hotel workers<a href="http://www.guardian.co.uk/world/2011/jun/07/hotel-workers-fury-strauss-kahn" target="_hplink"> reportedly</a> gather outside the Manhattan courthouse, where they shot their disapproval at Strauss-Kahn.

  • June 28

    After weeks of speculation, Christine Lagarde is <a href="http://www.huffingtonpost.com/2011/06/28/lagarde-imf-christine-elected_n_886148.html" target="_hplink">formally appointed</a> to replace Strauss-Kahn as IMF managing director.

  • July 1

    Strauss-Kahn walks out of court without bail and free from house arrest after prosecutors <a href="http://www.huffingtonpost.com/2011/07/01/dominique-strauss-kahn-released_n_888593.html" target="_hplink">acknowledge</a> there were questions about the credibility of the hotel housekeeper who accused him of sexual assault.