Cardinal Keith O'Brien, who heads the Roman Catholic Church in Scotland, said the requirement for priestly celibacy is "not of divine origin" and could be reconsidered.
He told BBC Scotland that "the celibacy of the clergy, whether priests should marry -- Jesus didn't say that."
He said that "many priests have found it very difficult to cope with celibacy," and while he had never considered marriage himself, "I would be very happy if others had the opportunity of considering whether or not they could or should get married."
O'Brien, 74, will form part of the conclave of cardinals that chooses the next pontiff, following the resignation of Pope Benedict XVI.
Benedict announced earlier this month that he will step down Feb. 28 -- the first pope to resign in almost 600 years.
The cardinal said that the next pope would be free to consider changing church policy on issues, such as celibacy for priests, that were not "basic dogmatic beliefs."
He said that "we know at the present time in some branches of the church priests can get married, so that is obviously not of divine origin and it could get discussed again."
In recent years a number of traditionalist Anglicans opposed to the ordination of women and other changes have joined the Roman Catholic Church. The pope granted special dispensation for married Anglican clergy to stay married and be ordained in the Catholic Church.
O'Brien also said it was time to think seriously about having a pope from outside Europe.
He said he would be "open to a pope from anywhere if I thought it was the right man, whether it was Europe or Asia or Africa or wherever."
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