In a newspaper interview, the cleric cited the success of smaller independent nations such as Ireland and Denmark to support his views.
He also voiced frustration with the current powers of Holyrood.
The 68-year-old's views have been welcomed by Scottish National Party leader Alex Salmond.
In an interview with the Catholic Herald newspaper, Cardinal O'Brien said: "I would not get too involved in the politics of independence, but I am happy that, if it is the wish of the people, Scotland becomes an independent country.
"There is currently some frustration among the Scots about the say they have over what happens here, and that is part of what is pushing the independence movement.
"I can see this coming, perhaps not in the next few years, but before too long."
The complete interview will be published next week in the Catholic Herald.
As far as the actual issue at hand, I have read opinions going in either direction. On the one hand, Scotland has provided the UK with a lot of talent over the years that would stay in Scotland and be used at home if Scotland were no longer a member of the UK. On the other hand, if Scotland remained in some kind of economic union with the rest of the UK and the EU, its talent would still be able to migrate out of the country, but the national programs that gave something back to Scotland would be gone. Could Scotland pull off an Ireland and be the next economic tiger of Europe? Aside from gneralizations by His Eminence, serious study would have to be made of the economic situation: skilled labor, tax incentives, trade agreements, etc.
Personally, I think it would be interesting if Great Britain was once again divided in two. If the Scots chose to keep the monarchy in their independence, England would once again be ruled by a Scottish monarch. Or they could put whichever of the Stuart claimants they preferred back on the throne.