Reports suggest that the High Court's judge Hugh Bennett has thrown out some of the claims made by Ms Mills in her claim for her share of McCartney's estimated pound stg. 825million ($2.05billion) fortune.
However, the couple's lawyers issued a joint statement urging against misreporting of the case. It added: "The parties both ask the media to respect their privacy and the confidentiality of the proceedings, as they work to settle the outstanding issues between them in their divorce."
The hearing, which started on Wednesday and is thought to have concluded yesterday, is believed to be a preliminary action before the main divorce case this year.
The couple announced the end of their marriage last May. They did not sign a prenuptial agreement before their wedding in 2002.
In August, Ms Mills was allegedly locked out of their pound stg. 7million home in St John's Wood, northwest London, with their two-year-old daughter, Beatrice. A newspaper photographer recorded the scene.
The McCartney camp later accused Ms Mills of stage- managing the event to generate sympathy.
Two months later, a copy of Ms Mills's divorce papers was leaked to the media. In them, McCartney was accused of verbally and physically abusing her. McCartney, 64, denied the allegations.
He looked relieved as he left the Royal Courts of Justice just before noon, made his customary victory sign at the media and climbed into a car.
Ms Mills, 39, left the court soon after through the back of the building, using a private judges' exit, and was ushered into the front seat of a waiting, chauffeur-driven car.
She walked impassively, her eyes hidden behind dark glasses, past the media without offering any comment.
None of the lawyers would confirm that the present proceedings were over, but all the legal documents were removed from the courtroom and the case was not listed by the court to continue.
