Police questioned the Socialist politician's daughter and her mother, his ex-wife Brigitte Guillemette, on Friday over claims by French writer Tristane Banon that he tried to rape her in 2003, said the source, who asked not to be named.
Guillemette is Banon's godmother and Camille Strauss-Kahn was a friend of Banon, now 32, at the time of the alleged attack, which Banon says took place as she tried to interview Dominique Strauss-Kahn for a book.
Police also questioned Banon and her mother, Socialist politician Anne Mansouret, last week.
Mansouret has said recently in several press interviews that she had contacted Guillemette shortly after the alleged sexual assault on her daughter.
Strauss-Kahn has dismissed the alleged attack as "imaginary" and his lawyers are counter-suing Banon for alleged defamation.
Strauss-Kahn is in New York pending legal proceedings for allegedly sexually assaulting and trying to rape a hotel maid there. Prosecutors have admitted doubts about his accuser in that case, raising the prospect of his acquittal.
French detectives are also expected to question Francois Hollande, a leading candidate for the opposition Socialists' nomination to run for president of France next year.
Banon has said Hollande knew of her claims at the time of the alleged attack but he has denied having any detailed knowledge of it. Le Figaro newspaper said Hollande may be questioned in September.