The source specified that the high-profile French couple, both 63 years old, are living at two different residences in Paris, and added that Strauss-Kahn is "well" despite this "difficult" period in his life.
The French economist, tipped to have been the Socialist Party's presidential candidate until becoming engulfed by a string of sex scandals, has been separated from his wife of 20 years for a month to six weeks, the source told AFP, speaking on condition of anonymity.
Strauss-Kahn and Sinclair, a leading French journalist, returned to Paris in September after scandal cost Strauss-Kahn his post as managing director of the International Monetary Fund (IMF) and ruined his presidential ambitions.
After three and a half years at the helm of the IMF, he resigned on May 18 2011, four days after a Guinean housekeeper at New York's Sofitel Hotel, Nafissatou Diallo, accused him of sexual abuse.
The criminal case was dropped in August 2011 after the prosecutor expressed doubts about Diallo's credibility, but a civil suit is still pending in New York.
Strauss-Kahn admitted to having a brief "inappropriate" sexual encounter with the alleged victim but denied all accusations of violence or constraint.
Sinclair was a stoic defender of her husband throughout his very public trial, which caused anger back in France when Strauss-Kahn was given the "perp walk" and paraded in front of TV cameras in handcuffs.
Sinclair, who is currently heading the French edition of The Huffington Post online news site, said at the start of his trial that she didn't believe "the accusations brought (against her husband), not for a second."
Life has not become any easier for the couple since criminal proceedings in New York came to a close.
On March 26, a French court questioned Strauss-Kahn regarding his alleged involvement with a prostitution ring running out of the Carlton Hotel in the northern city of Lille.
In May, the city's public prosecutor ordered a preliminary investigation into events "that could be qualified as gang rape" that allegedly occurred in Washington in December 2010, as part of the case.
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Lawyers in France announced on Friday that the couple was suing the magazine Closer, which was first to report that they had split up.
"Dominique Strauss-Kahn and Anne Sinclair decided to sue this publication for an invasion of privacy," lawyers said. "A summons will be delivered shortly to the Paris district court."
Aides for the couple declined to answer AFP when questioned Friday on the matter.