If Prince William's first child is a girl, she will accede the throne under proposed changes to succession laws, supported by the Queen.
The 85-year-old monarch has indicated she supports moves to repeal the primogeniture law, which puts male heirs ahead of their older sisters, as is the case with Princess Anne and her younger siblings, Prince Andrew and Prince Edward.
British newspaper the Sunday Telegraph reports the Queen has encouraged Prime Minister David Cameron to pursue the issue at the Commonwealth Heads of Government Meeting (CHOGM) to be held in Perth late this month.
"The Queen will naturally leave the politics and the debating to her Government, but she has let it be known that she would very much welcome an active debate on the issue by all her Commonwealth leaders," an unnamed palace source told the Telegraph.
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Under a plan formulated by Cameron, succession to the throne would be determined simply by the order of birth.
The necessary reforms would require agreement among the 15 realms of which the Queen is head of state, including Australia and New Zealand.
Cameron has also indicated hopes to repeal the ban on a King or Queen being married to a Catholic.
"This rule is a historical anomaly. It does not, for example, bar those who marry spouses of other faiths and we do not think it can continue to be justified," Cameron has written.
The Queen and Prince Philip, 90, this week begin a 10-day visit to Australia, ending with CHOGM's opening.