Archbishop Conti, who for 25 years was Bishop of Aberdeen prior to his Glasgow appointment, is required by church law to submit his resignation to Pope Benedict XVI once he reaches his 75th birthday, a milestone he hits on March 20th.
However, the timescale and secret processes involved in appointing a successor can take some time and the Archbishop could still be in place for more than a year.
The news comes as the prospect of the first papal visit to Scotland in almost 30 years was raised after a formal invite by Scottish Secretary Jim Murphy.
Mr Murphy, who has also invited President Barack Obama for an official visit, has spoken to the prime minister about a Scottish visit by Pope Benedict XVI, after Gordon Brown invited him to the UK during a Vatican meeting.
Mr Murphy said it would be for Downing Street, Buckingham Palace and the Vatican to work out the details of any visit, but that the feedback so far had been "positive".
Archbishop Conti was appointed to Glasgow by Pope John Paul II in 2002 following the sudden death of the iconic Cardinal Thomas Winning.
In his seven years, he has created a "wish list" of projects including the much-needed renovation of St Andrew's Cathedral on Glasgow's Clyde Street at a cost of several million pounds, and the creation of an Italian Garden in honour of the Italian role in the Archdiocese over the years.
Archbishop Conti also commissioned artist Peter Howson to create a huge painting with upwards of 600 figures to hang in a focal point in the cathedral when the renovations are completed.
It is expected to be the largest crowd scene ever painted in Scotland and the most important commission for a Scottish Catholic cathedral since the sixteenth-century Reformation.
One name already in the frame to succeed him is Bishop Philip Tartaglia of Paisley. Watchers of Catholicism in Scotland claim he has all the qualities and the background for the job, having been born in Glasgow and ordained priest for service in the archdiocese.
He is also seen as a possible candidate to head a Vatican Congregation, which carries with it the reward of a Cardinal's "red hat", such is the esteem within which he is held in the Vatican.
However, when the process is up and running it will be totally secret. A parallel process is under way in London after Cardinal Cormac Murphy-O'Connor reached his 75th birthday.
Pope John Paul II made a six-day trip to Scotland in 1982, which included mass in Bellahouston Park in Glasgow attended by about 300,000 people.
The date of any UK visit is not clear, although the Prime Minister has said the Pontiff could visit as soon as he wanted. The 81-year-old pope is due to visit Cameroon and Angola later this month, with a trip to Israel also planned for later in the year.
A spokesman for the Catholic Church said it was too early to say what form any proposed visit will take. "We would absolutely welcome the possibility of a visit by Pope Benedict XVI," he said.
"But, of course, we appreciate there are many other countries who have never had a papal visit and would like one."
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(Source: GUK)