Archbishop Leo Cushley told a newspaper his "impression" was that Rome had finished with the matter.
Cardinal O'Brien, who was Britain's most senior Catholic cleric, stepped down in February after three priests and a former priest made allegations of inappropriate behaviour against him.
He issued an apology, saying ''there have been times that my sexual conduct has fallen below the standards expected of me''.
After his resignation from the Archdiocese, he stated that he would play no further part in the public life of the Catholic Church in Scotland. He later left the country for a period of ''spiritual renewal", with reports suggesting the Vatican had ordered him to leave.
In the Scotland edition of the Times today, Archbishop Cushley suggested that the Vatican would not be pursuing any further action in relation to the Cardinal.
The Archbishop told the newspaper: "My impression is that Rome has finished with this. They will monitor the situation.
"They will look into it again after a certain period to see that things are going in they way they ought to be going. They may consider other evidence if it comes to light, but it would be up to them as to what they should do."
On the prospects of Cardinal O'Brien coming back to Scotland soon, the Archbishop added: "He will not return to Scotland. Nothing is a lifetime sentence but it is a reasonable assumption that he will not be coming back in the near future."
Cardinal O'Brien stepped down after 27 years amid the claims of inappropriate behaviour dating to the 1980s.
He left Scotland in May for a period of ''spiritual renewal, prayer and penance'' after it was reported he was planning to settle in Scotland.
When he resigned, he issued a statement saying: ''I wish to take this opportunity to admit that there have been times that my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal."
The cardinal had been Archbishop of St Andrews and Edinburgh since 1985.