Gordon Brown has opened talks with Buckingham Palace on removing the 308-year-old law which bars members of the Royal Family from marrying Roman Catholics.
The Princess Royal would jump ahead of the Duke of York if the law on succession are overhauled
Discrimination against female heirs to the throne would also be scrapped under the proposals expected to be introduced next year, if the law were to be made retrospective the Princess Royal would move ahead of the Duke of York in the line of succession.
At present, members of the Royal Family are forbidden by the Act of Settlement from converting to Roman Catholicism or marrying someone from the Catholic faith unless they agree to being removed from the order of succession.
Male members of the Royal family take precedent over their female relatives, meaning that the Princess is further down the line of succession than her younger brothers and their children.
The Prime Minister is understood to be in favour of overhauling the laws on succession, and Buckingham Palace is also thought to be ``open'' to the plans.
Two of the main impediments to reform - the need to secure the consent of the Commonwealth, and concerns about the monarch's status as head of the Church of England - have both been discussed.
Monarchs and members of their family in the order of succession have been banned from marrying Roman Catholics since the Glorious Revolution of 1688, when the Catholic James II was overthrown in favour of the Protestant William of Orange. The prohibition is enshrined in the Bill of Rights passed that year, and the 1701 Act of Settlement.
Rewriting the Act of Settlement requires the consent of all 53 Commonwealth countries, and Mr Brown hopes to discuss the proposal at the Commonwealth summit in November. He has already held private talks about his plans with some Commonwealth leaders.
Sources close to the Prime Minister stressed that the plans would not undermine the Establishment of the Church of England, and that the monarch would retain the role of head of the Church.
If the law was changed and it is made retrospective, the Princess would move from 10th to fourth in line to the throne, behind her older brother, the Prince of Wales, and his sons, Princes William and Harry.
Her children, Peter and Zara Phillips, would also be lifted up the line of succession, ahead of the Duke and his daughters Princesses Beatrice and Eugenie, and the Earl of Wessex and his children, Lady Louise Windsor and Viscount Severn, who would move after his older sister.
During the current Queen's reign, two members of the Royal Family - Prince Michael of Kent and the Earl of St Andrews - renounced heir rights of succession after marrying Roman Catholics. Last year, it was announced that Autumn Kelly had renounced her Catholic faith before she was able to marry Mr Phillips.
Over the past decade, Labour has pursued a number of policies which have angered Catholics, such as equality laws which forced adoption agencies to consider homosexuals as potential parents and the creation of hybrid human-animal embryos.
Mr Brown's bid to rewrite the Act of Settlement is thought to be part of a new attempt to win over Catholics and pave the way for a state visit to Britain by Pope Benedict XVI.
The Prime Minister is also said to be considering offering a peerage to Cardinal Cormac Murphy-O'Connor, the head of the Roman Catholic Church in England and Wales, which would make him the first Roman Catholic bishop to sit in the House of Lords since the Reformation.
Speaking about the Act of Settlement yesterday during an event at the House of Commons, the Cardinal said: "It's discriminatory. I think it will disappear, but I don't want to cause a great fuss over it."
In Sweden, the law was changed in 1980 to allow the succession to pass to the eldest child of the monarch regardless of gender, while similar moves were made to the royal families of Belgium, the Netherlands and Sweden.
MPs will today[Friday] be given the opportunity to vote on reforming laws proposed by a backbench MP to allow Roman Catholic succession.
The Private Member's Bill is being introduced by Evan Harris, a Liberal Democrat, and enjoys cross-party support. As well as the backing of senior Catholics in the Commons, including Edward Leigh, the Tory chairman of the Public Accounts Committee, and Andrew MacKinlay, Labour MP for Thurrock, it is also supported by a number of women members.
The Prime Minister will not support this legislation himself as he has concerns about some technical aspects of the way it has been drawn up, however, Labour MPs are free to vote in favour if they wish. Instead, the Prime Minister will wait until after negotiations are concluded before introducing his own legislation next year.
A Number 10 aide said last night: ``In principle this is an area where we want to see progress. We are not going to support today's Bill but we won't oppose it. It is not possible to simply change legislation as it's a very complex area.''
Dr Harris said of his Bill: "The Bill will remove the uniquely discriminatory stipulation which currently exists - that an individual in the line of succession to the throne can have a civil partnership with a Catholic, can marry a Muslim or atheist, but can not marry a Catholic.
"It will also end the rule of primogeniture, whereby women in the line of succession to the throne is automatically superseded by a younger male sibling - if your current monarch had a young brother, we would never had had a Queen Elizabeth II."
The Bill would also repeal the Royal Marriages Act of 1772, which requires the descendants of George II to seek the consent of the monarch before marrying if they are under the age of 25.