Reports that Cardinal William W. Baum had a 30-minute private audience with Pope John Paul II last week before leaving Rome have stirred speculation that the Washington prelate may be headed for a Vatican post.

A spokesman for Cardinal Baum, who returned to Washington on Sunday, said that speculation that the cardinal is headed to the Vatican is untrue.

The Rev. Maurice Fox, director of the office of communications for the Archdiocese of Washington, said yesterday that "Cardinal Baum has not been given any position in the Vatican or Curia. It is common for a cardinal to have a visit with the pope when leaving Rome."

Vatican watchers have long considered Baum unusually qualified for a post in the Curia, the administrative core of the Vatican. Even though, at 51, Baum is the youngest American cardinal, he is unquestionably one of the best qualified of the Americans to fill a top Vatican post.

He has a well deserved reputation as a scholar. His doctorate is in sacred theology but he is equally at ease in the most erudite conversations on philosophy, church history or the arts. He is a linguist, fluent in Italian and French as well as Latin.

He is familiar with the Vatican, having served during the Second Vatican Council as a peritus, or adviser, one of the corps of younger theologians who helped draft the documents ultimately adopted by the bishops and thereby playing a crucial role in the shaping of the church.

Since being named a cardinal in 1976 he has been a member of two Vatican departments; the Sacred Congregation for the Doctrine of the Faith and the Sacred Congregation for Catholic Education, journeying to Rome two of three times a year for congregational meetings.

A fellow member of the Congregation for Catholic Education was the Polish Cardinal Karol Wojtyla, now Pope John Paul II.

But Baum's acquaintance with the new pope goes far beyond exchanges on ecclesiastical committees. The two cardinals have hosted each other in their respective homes; concelebrated mass at each other's cathedrals. Baum was the host when the Polish cardinal visited here in the summer of 1976, and Wojtyla when Baum visited Poland earlier this year.

The precedent for an American to head one of the nine congregations or the three secretariats at the Vatican was established in 1969, when Pope Paul named Cardinal John Wright to head the Sacred Congregation for the Clergy.

Wright, at 69, is still six years under what Pope Paul set as retirement age for bishops. But he has been troubled for several years with cataracts and, more seriously a progressively disabling neurological condition that forced him to miss the funeral of Pope Paul and the August conclave of cardinals.

Unlike his predecessor, Pope John Paul II has thus far reappointed only three curial incumbents: Cardinals Jean Villot, Pericle Felici and Sebastiano Baggio.

There are two, possibly three, high Vatican posts being mentioned frequently as likely spots for Baum: as head of either of the two congregations of which he is a member, or as president (administrator) of the Secretariat for Christian Unity.

Christian Unity has been headed for a decade by a scholarly and widely respected Dutchman, Cardinal Johannes Willebrands. But in 1975, Willebrands was named primate of his native Netherlands, and has had to divide his time between the two posts since.

Baum was the first man to head the ecumenical and interreligious affairs division of the U.S. Catholic hierarchy from 1964 to 1967, in the flowering of Catholicism's first overtures to the "separated brethren," as Valtican II called other Christian communions. His experience from this period, plus his continuing interest in ecumenism, would make him uniquely qualified for the unity secretariat.

Individuals at the highest levels of the church in this country universally plead total ignorance of any pontifical plans for the Washington cardinal. But at the same time, they remain fascinated with the speculations.