Ever since he was plucked six years ago from a remote southeast Missouri diocese to head, at the age of 46, the Archdiocese of Washington, William Wakefield Baum has been marked as a comer in the Roman Catholic Church.

Speculation that Baum might be destined for a Vatican post began in earnest when he was elevated to the College of Cardinals three years later. At 49, he was one of the youngest men ever elevated to the Cardinalate.

Now, three years later, he is still in Washington, but speculation that Baum is slated for a post in the Roman Curia, the administrative heart of the Vatican, persists.

In fact, in the Catholic subculture where such rumors flourish, the speculation centers on who might succeed Baum as head of the Washington archdiocese when -- not if -- the cardinal is called to Rome.

The already substantial argument that Baum, who will be 53 next month, is bound for the Curia was strengthened last summer with the death of Cardinal John Wright. Wright, who headed the Vatican Congregation for the Clergy, was the only American in the Vatican leadership.

It is unlikely that the American Catholic church, the third largest in the world and major source of Vatican income, would be unrepresented for long in the church's top decision-making body.

Of all the American cardinals, Baum seems the most likely candidate for a Vatican appointment.

He is a theologian as well as an expert on church history and philosophy. He is fluent in Latin and Italian -- prerequisites for a Vatican official -- and speaks passable French.

During the second Vatican Council (1962 to 1965), the then monsignor Baum was invited by his bishop, the most Rev. Charles Helmsing of Kansas City, to act as a peritus, or theological advisor. In Helmsing's services, Baum learned the ropes of Vatican politics and distinguished himself as a scholar. He helped draft the Decree on Ecumenism, one of the major documents of the council.

In the years since Pope Paul VI named Baum a cardinal, he has naturally gotten more deeply involved in Vatican affairs. He is a member of three of the 12 key Vatican divisions; the Secretariat for Non-Christians, the Congregation for the doctrine of the Faith and the Congregation for Catholic Education.

Through his work in the latter post, he came to know Cardinal Karol Wojtyle, who last year became Pope John Paul II.

In 1976, Baum served as host to Wojtyla during his visit to Washington following the Eucharistic Congress in Philadelphia. Wojtyla returned Baum's hospitality when the Washington cardinal visited Poland.

Baum, who has a quiet reputation as a patron of the arts, gives private musicals in his home from time to time. As head of the archdiocese, he has sponsored a number of art exhibits.

As executive director of the Committee for Ecumenical and Interelgious Affairs for the American Catholic hierarchy, from 1964 to 1967, Baum developed friendships and working relationships with many Protestant and Eastern Orthodox leaders.

This ecumenical job, an outgrowth of the Second Vatican Council document that he had helped to write, earned him a reputation as something of a liberal in the tumultous post-Vatican II years.

But, as cardinal-archbishop of the Washington diocese, he has moved inexorably to the centrist-to-conservative position in church affairs. Today, his position would vary little on most issues from that of the solidly traditional John Paul.