On the eve of his departure to Rome where he will help select the next Pope, Cardinal O'Brien, who leads the Catholic Church in Scotland, said many priests struggle to cope with celibacy and should be given the choice to marry.
The cardinal is understood to have expressed a long-held personal view and will have supporters among fellow members of the conclave that will elect the successor to Pope Benedict XVI.
He said: "I'd be very happy if others had the opportunity of considering whether or not they could or should be married. It's a free world and I realise that many priests have found it very difficult to cope with celibacy as they lived out their priesthood, and felt the need of a companion, of a woman, to whom they could get married and raise a family of their own."
Professor Tom Devine, Scotland's leading historian and authority on Catholic matters, described the comments as "a most significant intervention from the Scottish Catholic hierarchy".
Others have insisted Cardinal O'Brien's views are "not an aftershock" following the Pope's dramatic decision to resign last week and while they are already attracting worldwide interest, will not lead to any change in Catholic laws on celibacy.
The comments have also been seen in the context of the cardinal's intention to stand down from all frontline duties in the near future. He turns 75 next month and is required then under canon law to submit his resignation. He has also been suffering from ill-health in recent times.
He has already quit as president of the Bishops' Conference of Scotland, the key decision-making body in the Church.
The comments are likely to spark discussion on the nature of celibacy, the isolation of the priesthood and inevitably abuse within the clergy, as well as the need to attract new members to the priesthood, particularly in Africa where young marriage is more commonplace.
However, sources insist the cardinal's comments are not a pitch for votes among the more liberal cardinals in next month's conclave but are more a product of "being demob happy" than an attempt to be Pope.
Allowing priests to marry would break with rules that have applied in Western Catholic churches for nearly 900 years. Married Anglican vicars have been able to convert and join the Roman Catholic priesthood since the 1950s and in 2009 the Church extended this to also allow ordinary married Anglican converts to become priests.
Theoretically, because the rule of clerical celibacy is a law and not a doctrine, exceptions can be made, and it can in principle be changed at any time by the Pope. However, both Pope Benedict XVI and his predecessor insisted on the traditional practice, making Cardinal O'Brien's comments all the more radical and dramatic.
The cardinal added: "I would like others to have the choice. In my time there was no choice, you didn't really consider it too much. It was part of being a priest when I was a young boy – priests didn't get married and that was it.
"When you were a student for the priesthood, well it was part of the package, as it were, that you were celibate, that you didn't get married and you didn't really consider it all that much, you just took your vows of celibacy the way someone else would naturally take their vows of marriage."
Liz Leydon, editor of the Scottish Catholic Observer, said: "The cardinal is nearing his retirement and has very forthright views. This must be something he has given some thought to."
Professor Devine said it was impossible to know whether Cardinal O'Brien spoke for himself alone or for a wider constituency.
He added: "Does he know something the rest of us do not? Whatever the case, this is a most significant intervention from the Scottish Catholic hierarchy, often seen by observers as one of the most loyal to Rome.
"Whatever the future of clerical celibacy, I think many Catholics would at least welcome an open debate on the subject. After all, the law is a discipline, not dogma, and hence subject to change and fresh interpretation.
"The Church teaches that the priesthood is a ministry formed by the life on Earth of Jesus Christ of which celibacy was a part. Will this teaching remain the basis of the established order while the people of the Church in Europe cry out for more priests?"
John Haldane, professor of Philosophy at St Andrews University, said there was no possibility of there being any change to the Catholic Church's position so far as clergy marrying is concerned and was sceptical about the significance of the comments.
Mr Haldane, who has recently written on the merits of allowing married men to be ordained to the Catholic priesthood, said: "There is no way the Church is ready to depart from what it regards as apostolic tradition. While I have some doubts as to whether the cardinal intended his comments to be taken as they have been reported, I do believe he would be open to looking at the issue."