Officials at the solicitor-general's office were not immediately available Sunday for further comment.
The government is expected to use new equality legislation to guarantee women's succession rights, the Times report said.
Queen Elizabeth II succeeded to the throne only because she had no brothers.
When the queen's daughter, Princess Anne, was born, she was third in line to the throne, behind her mother - then Princess Elizabeth - and her brother Prince Charles.
As her brothers Andrew and Edward were born, Anne dropped down the line of succession, where she is currently 10th.
Opposition Liberal Democrat equalities spokeswoman Lynne Featherstone agrees the rule should be "confined to the dustbin of history."
"This is the perfect time to do this when there is no one who will be affected," Featherstone was quoted as saying by the newspaper.
The report says Baird also wants to repeal the law banning the heir to the throne from marrying a Catholic.