The investigation was opened on July 28 after a former shareholder in a now-defunct Luxembourg-based firm, LSK, lodged a formal complaint.
Strauss-Kahn, once tipped as a future French president, was forced to resign from his role as head of the IMF in 2011 after being accused of sexual assault by a New York hotel maid.
Those criminal charges were dropped in 2012 and the case was settled in a civil suit.
The probe into Strauss-Kahn's business dealings in Luxembourg focuses on a former shareholder, Jean-Francois Ott, who pumped 500,000 euros (USD 570,000) into the company.
Ott claims he was given a misleading impression of the firm's financial situation when he made the cash injection and has sued the company, and some of its former administrators, including Strauss-Kahn, for fraud.
Strauss-Kahn had hoped to build up LSK into a USD 2.0-billion-dollar investment fund, but winding-up proceedings began in November 2014 after its founder, Thierry Leyne, committed suicide in Tel Aviv.
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