The cardinal, who admitted sexual misconduct with priests after resigning earlier this year, was ordered by the Vatican to leave Scotland in May for a period of spiritual renewal and penance.
He stood down following allegations made by three priests and a former priest of “inappropriate” behaviour in the 1980s, and later admitted his sexual conduct had “fallen beneath the standards” expected of him.
Monsignor Leo Cushley, a veteran Vatican diplomat who will be installed as the new archbishop on Saturday, said it was “not impossible” that the cardinal would return to Scotland one day, but he did not believe it was likely or desirable.
He told BBC Radio 4's Sunday programme: "He is a free man in a free country so he can come back if we wants. But the Holy See will be the one to ask him to do whatever it is they intend.
"We all have our own opinions about that and what would be best for him, what would be best for those affected his actions, what would be better for the local church.
"What can I say? I think it's not impossible for Cardinal O'Brien to come back to Scotland, of course it's not impossible, but personally speaking I think it's somewhat unlikely that he would return to Scotland.
"There would be a number of reasons for that, and looking around myself I think it would probably be wiser and more helpful for the future of the Church here if he were not to be back in the country."
Mgr Cushley added that he did not believe it was necessary for investigators to be sent from Rome to restore the confidence of Roman Catholics in Scotland as the cardinal was “no longer on the Scottish landscape”.
"From what I understand, I think the Holy See already has enough of the story to work on, and to talk of an independent inquiry into the actions of this man when we are not talking about anything that is criminal seems a little bit exaggerated to me.”
The archbishop-elect's ordination will take place in St Mary's Cathedral in Edinburgh on Saturday.
He told Scotland on Sunday that he planned to work “quietly and patiently” to rebuild relationships in the diocese, adding: “My first priority is to get to know and appreciate the priests of the diocese and by doing that I’m going to find out quite quickly, if I do it well, what has been going on and what has been happening.
“I want to, quietly and patiently, rebuild trust within the clergy, but that does not mean that there will not be room for governance. There needs to be a new sense of direction.
“That will not come about only through gentleness and understanding of the situation, but through a certain amount of firmness and that was also something I heard in my discussion with the Holy Father.”
Mgr Cushley said he did support the idea of an independent inquiry into the Catholic Church’s handling of child sex abuse cases following revelations of historic abuse at the Fort Augustus Abbey boarding school in the Highlands.
The new archbishop was born in Airdrie, North Lanarkshire, and has spent the last 20 years working in the Vatican’s diplomatic service.
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