In an interview with BBC Scotland, O'Brien, the most senior Catholic cleric in Britain, pointed out priests were allowed to marry for centuries. The church also has allowed married Anglican and Lutheran priests who converted to become Catholic priests.
O'Brien will be among the cardinals who gather in Rome to choose a successor to Pope Benedict XVI. Benedict leaves office next week, the first pope to retire in 600 years.
In the interview, O'Brien said he does not believe every issue is up for grabs. He described the church's ban on abortion and euthanasia as being "of divine origin."
But he said other church practices do not have biblical roots.
"For example the celibacy of the clergy, whether priests should marry -- Jesus didn't say that," he said. "There was a time when priests got married, and of course we know at the present time in some branches of the church -- in some branches of the Catholic church -- priests can get married, so that is obviously not of divine of origin and it could get discussed again."
O'Brien said he would be willing to vote for a pope from outside Europe. Possible candidates have been suggested from Africa and South America.