Former IMF chief Dominique Strauss-Kahn and his wife Anne Sinclair have reportedly been living apart for a month now, (Lucas Jackson/Reuters)

Former IMF chief Dominique Strauss-Kahn, who is under investigation for links to a prostitution ring, has separated from his wife according to the French magazine Closer.

The couple have not confirmed their separation, and say they're filing a lawsuit against the magazine after it posted the report online Thursday.

Anne Sinclair, Strauss-Kahn's wife of two decades and once a diva of French journalism, was stoic last year as he faced allegations by a New York hotel maid of sexual assault. The charges were dropped but he faces a civil lawsuit in that case.

Closer said Sinclair had asked Strauss-Kahn to leave a month ago. It cited no sources.

A statement Friday by Henri Leclerc and two other attorneys said the couple "decided to file suit against this publication for invasion of privacy." It made no mention of a separation.

"For me, it is a definitive breakup," Laurence Pieau, Closer’s executive editor, told the New York Times in an interview on Friday.

While Strauss-Kahn fights the latest charges against him, his wife has taken up a new job as the online editor of the French edition of the Huffington Post.

Strauss-Kahn resigned his position as head of the IMF after he was charged with sexually assaulting a housekeeper in a New York hotel last May. The criminal charges were later dismissed.

The housekeeper filed a civil suit against Strauss-Kahn in New York seeking unspecified damages, while he countersued for malicious prosecution and defamation.

Sinclair was steadfast in her support of her husband, even when the couple returned to France last fall, only to be hit with another rape allegation by a young French woman. Those charges were also dropped.

Then in March, he was charged with involvement in an alleged prostitution ring operating in the northern French city of Lille. Police are also investigating allegations that he sexually assaulted a Belgian prostitute at a hotel in Washington D.C. in 2010.