Barbara Charone, Madonna's spokeswoman in London, declined comment on the reports. Ritchie's mother, Lady Amber Leighton, told reporters the family wouldn't be making any statement.
This is the second time this year that the superstar couple's marriage has come under the media microscope. Over the summer, Madonna was linked - unfairly, she said - to the breakup of New York Yankee Alex Rodriguez and his ex-wife Cynthia.
In July, Madonna's U.S. publicist released a statement that said the singer and Ritchie had "no plans to divorce."
Madonna and Ritchie married in December 2000 at a Scottish castle. The couple have two children: Rocco, 8, and David Banda, 3, who was adopted from Malawi in 2006. Madonna also has a 12-year-old daughter, Lourdes, from her relationship with personal trainer Carlos Leon.
The couple are reportedly worth some $525 million, the bulk of that belonging to Madonna. Ritchie has an estimated $35 million fortune. They own homes in London, Los Angeles and New York, and a 1,200-acre retreat in Wiltshire, England.
Madonna will perform concerts Wednesday and Thursday in Boston as her "Sticky and Sweet" tour continues. Ritchie's latest movie, "RocknRolla," recently opened to mixed reviews.
Lawyers said that if the divorce is confirmed, the couple would likely try to come to an agreement before heading to court.
"The judgment of the court would be to try and assess what they came in with and divide what they built up fairly equally," said David Allison, a lawyer with Family Law in Partnership, a London firm.
Ritchie's career has faltered during the marriage, while Madonna's songs, videos and concerts remain popular worldwide.
The needs of the couple's children will also be factored by the court, as they were in Britain's latest high-profile celebrity divorce, the battle between former Beatle Paul McCartney and model Heather Mills. In that case, McCartney and Mills fought over money and custody of their young daughter.
Mills received 24.3 million pounds in the divorce after four years of marriage.
"The needs of children figure quite highly, and that was one of the reasons Heather Mills got a gigantic amount of money, despite the fact that the bulk of Sir Paul's money was made before the marriage," Allison said.
Associated Press Writer Katy Daigle contributed to this report.