Princess Anne has slipped further down the line of succession
A 300-year-old law which gives males precedence in the royal line of succession could be abolished.
MPs are expected to use new equality legislation to guarantee a monarch's daughter equal claim to the throne.
Solicitor General Vera Baird said the male right to succeed ahead of an older sister was "unfair".
She told the Sunday Times that she also wanted to repeal the law forcing royals marrying Catholics to renounce their place in the line of succession.
The current law, the 1701 Act of Settlement, means male heirs take precedence over the British throne.
When Princess Anne was born she was third in line to the throne, behind her mother the Queen - then Princess Elizabeth - and her brother Prince Charles.
As her brothers Andrew and Edward were born she dropped down the line of succession, where she is currently tenth.
A draft of the Single Equality Bill is due to be published later this year.
Andrew Mackinlay, the Labour MP for Thurrock who has previously raised the issue with successive prime ministers, welcomed the move but said changing the law could be difficult.
Under the Statute of Westminster 1931 any change would have to be agreed by the parliaments in all countries which have the Queen as head of state.
The Queen is head of state of the UK and 15 other Commonwealth realms, including Australia and Canada.
Mr Mackinlay said Ms Baird was "naive" if she believed Westminster could change the rules on its own.
Shadow justice secretary Nick Herbert said there was "a strong case" for the law change.
But he said it would also raise complicated issues.
Mr Herbert said: "Other countries where the Queen is head of state will be affected by these proposals, and lifting the prohibition on heirs to the throne from marrying Catholics is not straightforward as it raises broader issues relating to the established Church.
"The government should publish a consultation document so that these matters can be debated properly and the Anglican Church and others can be consulted."
Liberal Democrat equalities spokeswoman Lynne Featherstone welcomed the proposed change.
She said: "We can't have a law that is meant to fight discrimination and injustice but allows a blatantly sexist law on royal succession to continue.
"This is the perfect time to change the law - when there is no-one who will be personally affected. Let's confine this outdated message that men are better than women to the dustbin of history."