Abedin filed for divorce in May, hours after Weiner pleaded guilty to sexting with a minor.
"In order to ensure the proceedings have a minimal impact on their child, the parties have chose to attempt to reach a settlement swiftly and privately", Ms Abedin's laweyer, Charles Miller, told the Post.
Huma Abedin and Anthony Weiner's divorce can be called a lot of things: "Messy" comes to mind, and definitely "sordid".More news: Newcastle United's Peter Beardsley to take leave amid racism and bullying claims
Abedin's lawyer issued a statement about the decision, noting the two will settle the divorce privately.
In a statement to the New York Daily News, Abedin's attorney said that's what's happening, for the sake of their 6-year-old son.
Weiner was considered a rising star in the Democratic Party until the former NY congressman admitted in 2011 that he had been sexting multiple women and was forced to resign. In September, Weiner was sentenced to 21 months in jail for illicit online contact with a minor. The FBI concluded that neither Weiner nor Abedin had committed a crime in their handling of the email.