The move would lift the ban on religious ceremonies for the registration of gay unions imposed when Britain legalised civil partnerships six years ago.
The government may also propose scrapping the legal definition of marriage as a relationship between a man and a woman, allowing gay men and women to call their partners husbands or wives, the Sunday Times said.
Equalities minister Lynne Featherstone will launch a consultation on the issue soon.
Critics say restricting homosexuals to civil partnerships rather than marriage is a form of discrimination. If passed into law the plan would bring Britain closer to countries such as the Netherlands and Canada where gays can legally marry.
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