"I'm sort of looking forward to the moment when he walks out on stage," said CBS correspondent Charles Kuralt last week of one of the singular events he has anchored over the years. It is the appearance of the ever-debonair pianist Vladimir Horowitz on the stage of the Bolshoi Zaal (Great Hall) of the Moscow Conservatory Sunday in his native land for the first time in 61 years.

The event itself is extraordinary enough, with the most celebrated classical musician born in Russia in this century doing something he long had sworn he would never do: returning to his homeland. He departed for the West one evening at age 21 with his money hidden in a shoe.

In addition, the Horowitz recital will become an important international media event, to be televised live, or nearly so, to an estimated tens of millions of viewers in Europe, the Soviet Union, the Orient and the United States. It is believed to be the largest audience reached from the Soviet Union since the Moscow Olympics.

In the United States, the entire concert will be telecast in a special two-hour edition of CBS' "Sunday Morning." It will begin at the usual hour of 9 a.m., delayed two hours from the time of transmission from Moscow. Kuralt and Robert Northshield, "Sunday Morning's" senior executive producer, are to be in Moscow for the broadcast. It is thought to be the first full classical concert on an American commercial television network since CBS televised another Horowitz concert in 1968.

Horowitz and his wife Wanda Toscanini Horowitz arrived in Moscow yesterday for what will be a relatively full two weeks of activity. There will be meetings with students and professors at the Moscow Conservatory, site of the 1,800-seat concert hall. On Friday there is to be a rehearsal.

The Horowitzes are staying at Spaso House, the residence of American Ambassador Arthur A. Hartman, and will proceed from Moscow to Leningrad, where Horowitz will give another recital the following Sunday.

It is unlikely that many persons in either audience will have heard Horowitz in recital before. The pianist stipulated in his contract that ordinary music lovers and students should be significantly represented.

Horowitz, who is playing without fee and whose expenses will be shared by the American and Soviet governments, is traveling with his own Steinway piano and Steinway technician Franz Mohr.

Peter Gelb, who is Horowitz's manager and a vice president at Columbia Artists Management, said that until recently Horowitz seemed unbending in his determination never to return to Russia. As recently as 1980, the pianist declared, "I have no desire to return . . . I lost all my family there. I never want to go back and I never will."

Horowitz was the youngest of four children -- a "spoiled child," by all accounts, and a bit of a dandy. His father was a well-to-do Jew, a rare thing in the Ukraine of that period. He was an electrical engineer whose firm represented, among others, Westinghouse in Kiev.

But after the Bolshevik Revolution, it became clear to the young Horowitz that his future lay outside Russia. No less a figure than the great pianist and teacher Artur Schnabel heard the young man during a visit and told him it was essential that he leave. His family also had fallen on hard times; Horowitz recalled several years ago that "in 24 hours my family lost everything. With my own eyes I saw them throw the piano through the window, into the street! The Communist motto was 'Steal what was stolen,' so they stole everything."

Despite Horowitz's outspokenness over the years, Soviet officials have been persistent in their efforts to get him to return, Gelb said last week. Though the visit coincides with the signing of the new U.S.-Soviet cultural exchange treaty, Gelb said Horowitz "could go anytime."

Gelb said the Soviet Ministry of Culture and Goskoncert, its concert bureau, have shown "genuine concern that Horowitz be happy, so delighted are they that he will return."

The pianist first considered the Soviet trip after the success last fall of concerts in London and Milan. "I think that he found that he was at a new point in his artistic life," Gelb said. Horowitz found, said Gelb, that averse as he is to traveling, that trip went well, and it started him "thinking of what he hasn't done and what he would like to do."

Gelb said he made no effort to persuade Horowitz to make the Russian trip. "My role was simply to explain to him how it could be facilitated, and how his particular living requirements could be met."

The worldwide television broadcast was arranged by Gelb and Columbia Artists Management. It will use three satellites and a staff of 45. The satellite coverage will be coordinated by the BBC. The video will be handled by a Swiss firm, Polyvideo, and the audio will be handled by Deutsche Grammophon, for which Horowitz now records. It will be transmitted in stereo from Moscow, but not on CBS.

Kuralt said "Sunday Morning" will dispense with the news portion of the show entirely, barring some kind of emergency. Kuralt could recall only two other times when the program had dealt largely with a single subject: shows on Picasso and on Henry Moore. The only sponsor Sunday will be AT&T, which will limit its commercials to six minutes out of a possible 24 minutes, Northshield said.

The program is to be vintage Horowitz: Scarlatti, Mozart, Rachmaninoff, Scriabin, Schubert, Liszt and Chopin.