The court lists "Ciccone M L v Ritchie G S" as one of 17 cases for "matrimonial and civil partnership causes for pronouncement of decree." That means a judge is to grant the couple a preliminary divorce decree, or decree nisi.
After six weeks and a day, the couple will probably be granted a decree absolute and the divorce will become final.
It is unusual for the couple to attend court in such cases.
British media reported Thursday that the celebrity pair had reached a settlement which would see the pop superstar keep the majority of her estimated 300 million pound ($445 million) fortune and share custody of two of her children with her film-director husband.
The two boys would split their time between Britain and the United States, the papers said, while Lourdes — Madonna's 12-year-old daughter from a previous relationship with personal trainer Carlos Leon — will live with her mother in the United States.
Neither paper cited a named source for their reports and requests for comment from representatives for the couple were not immediately returned.
An agreement between the two would avoid an ugly, public and expensive courtroom battle like the one between former Beatle Paul McCartney and model Heather Mills. Mills has said the media coverage of the rancorous divorce had pushed her to the brink of suicide; McCartney compared the process to going through hell.
In recent years, however, the relationship was dogged by rumors that the pair had fallen out over Madonna's plans to adopt a second child from Malawi. Media reports over the summer — denied by Madonna — linked the singer to the breakup of New York Yankee Alex Rodriguez's marriage to his ex-wife Cynthia.