The proposal would also allow members of the royal family to marry Catholics without giving up their place in the succession and would remove the gender distinction so a sovereign's oldest child would be the heir to the throne, The Guardian reported.
Changing the 1701 Act of Succession is not going to be easy, the report said. It would affect the status of the established Church of England and has international implications, since the British sovereign is head of state in 15 Commonwealth countries.
Many politicians welcome the proposal.
"This is an overdue but welcome move," said Lynne Featherstone, Liberal Democrat spokeswoman on equality. "Whilst the hereditary principle itself is obviously still a bit dodgy, at least this modernization ends the outrageous discrimination against Catholics and women."
A spokesman for Cardinal Keith O'Brien, head of the Catholic Church in Scotland, said talk of repealing the 1701 law "has yet to be followed with action."
The Church of England was noncommittal.
"The church carries on and waits for something real to happen," a spokesman said.
Celebrity Families of 2014 [PHOTOS]