New York's Gov. Mario Cuomo last week publicly acknowledged what has been privately known all along: he's available. If the Democratic Party wants to draft him as the party's presidential nominee, he won't say no. This makes him the leading unannounced noncandidate, and puts him, if not squarely in the race, at least obliquely in the race.

A lively possibility comes to mind. The Democrats could wind up by giving the country a reprise of the convention of 1952. Gov. Cuomo could be cast in the role that was played 36 years ago by Gov. Adlai Stevenson of Illinois. The parallels are inexact, but the story is worth recalling.

The '52 conventions were my first conventions, and I went off to Chicago as bug-eyed as a boy at his first state fair. The Republicans' bloody fight between Dwight Eisenhower and Bob Taft had been good fun. The Democrats' fight over a ''loyalty oath'' for southern states promised a splendid brawl.

The overwhelming favorite as the Democrats gathered was Sen. Estes Kefauver of Tennessee. Harry Truman hated Kefauver, largely because Kefauver had whipped him decisively in the New Hampshire primary four months earlier, but rank-and-file Democrats appeared to love the gentleman from Tennessee.

Kefauver had worked diligently for the nomination. The Democrats held 14 contested primaries in 1952. Kefauver won 12 of them outright and finished second in the other two. He polled more than 3 million votes in these primaries, about 64 percent of the total. Nobody else was even close. In sixth place was Gov. Stevenson, who made no campaign of any sort.

Stevenson, like Cuomo, kept insisting that he was not a candidate for president, that he wanted only to be an effective governor of his state. His friends had put him on the primary ballots in Oregon and in Illinois, but Stevenson had not lifted a finger to encourage them. Then came the Chicago convention, and Stevenson, as host governor, made the welcoming speech.

What a speech! Here was a man of literacy, wit, good humor and sound rhetoric. Stevenson captivated the visiting press. We listened in rapt attention as he chided the just-departed Republicans:

''For almost a week, pompous phrases marched over this landscape in search of an idea, and the only idea they found was that the two great decades of progress in peace, victory in war, and bold leadership in this anxious hour were the misbegotten spawn of socialism, bungling, corruption, mismanagement, waste and worse. They captured, tied and dragged that ragged idea in here and furiously beat it to death.

''But we Democrats were not the only victims here. First they slaughtered each other, and then they went after us. And the same vocabulary was good for both exercises, which was a great convenience. Perhaps the proximity of the stockyards accounts for the carnage.''

Well! With that address the Kefauver candidacy began to unravel. It helped that Chicago's Jack Arvey had packed the hall with leather-lunged Stevenson rooters. It also helped that Truman behind the scenes did his damnedest to defeat the Tennessean. On the third ballot Stevenson went over the top. In November he lost to Eisenhower by 6.6 million votes; he carried only nine southern and border states.

Cuomo at his oratorical best is a magnificent speaker. He stands just outside a pathetically weak field of Democratic candidates, not one of whom has yet demonstrated presidential class. Over the next six months Paul Simon, Michael Dukakis, Dick Gephardt, Al Gore, Bruce Babbitt and Jesse Jackson could exhaust themselves in a campaign that could see no clear winner before the convention. In that event, let us listen for an echo. History has a curious way of repeating its most dramatic scenarios, and New York's globe-trotting governor is waiting in the wings.