FROM A DISTANCE, it appears that Mario Cuomo is slying maneuvering to run for president. The man who said last February that he wouldn't seek the Democratic nomination is traveling to the Soviet Union this week and is scheduled to deliver his maiden foreign-policy speech on Oct. 13 to the Council on Foreign Relations. He has also journeyed in recent months to Iowa, New Hampshire, Illinois, Florida, California, Indiana and Texas. And this past week, his staff penciled in three more states for October and a sojourn in Mexico in December.

Like a woman in a dimly-lit bar, Cuomo the non-candidate looks terrific to many Democrats.

But sitting at his desk in Manhattan last week, wolfing down three slabs of prosciutto-filled calzone, Cuomo looks like a man who wants only to be governor of New York. He is relaxed and mellow. Instead of bristling at reporters, as he did last fall when he was still a candidate, he's now loose and full of good humor. When a press posse cornered him the other day after his lunch with former senator Gary Hart and asked how Hart seemed, Cuomo deadpanned: "He seemed hungry. He had swordfish and two deserts."

So is this relaxed and mellow man running? The best answer at this point is probably: No, but . . . .

Pressed by a reporter who shared the calzone at his World Trade Center office, Cuomo playfully summons Mary Tragale, his secretary and executive assistant of 29 years. "Mary, why am I not running for president?" he asks.

"Because you don't have the time," answers Tragale, who is the only person allowed to peek at the daily diary entries Cuomo scribbles in a brown leather notebook.

"Is there even a place in the diary where I said I should run?" Cuomo asks the woman who types his musings. "Where's the closest I ever came?"

"Two weeks after you said no last February," she replies. "You wrote, 'Maybe I should have.'"

Cuomo winces, and laughs at this one small crack in his public resolve to concentrate on being governor of New York.

So what is this sphinx up to? Is Cuomo secretly scheming to run for president? The answer again seems to be: No, but . . . .

No, he has no intention of entering any primaries or caucuses. "The only motivation I can see for running is that this terrible task must be done and I can do it at least as well or better than anyone," he says while being ferried by a state helicopter from Manhattan to an appearance on Staten Island last week. "That to me is the only motivation, and I don't see it that way. You shouldn't see running for the presidency like winning a batting title. When you win a batting title, your pursuit is over. When you win the batting title in pursuit of the presidency, you've just begun to play."

And no, Cuomo says he doesn't want to play. Nor does he want to join the chorus denigrating the eight Democrats who are already chasing the presidency. He still believes that one of the eight will emerge -- as Jimmy Carter did in 1976 or as Gary Hart almost did in 1984 -- as a fresh face. "What they lack is not charisma but celebrity," he observes.

Cuomo is credible when he says he does not hunger for the office, and he agrees with the two principal arguments lodged against a belated late-primary bid (dubbed the "late, late Mario scenario" by Paul Taylor of The Washington Post). He agrees it would be "arrogant" for anyone to parachute into the race at the end of the process -- "It would be unfair to the candidates who schlepped through the primaries." Cuomo also agrees that on most national issues he is a blank slate, famous for a single keynote address to the 1984 Democratic Convention: "I have a terrific record as governor. People in Iowa don't know that."

The final reason Cuomo isn't likely to run is the simple fact that he's said he won't. He is a stickler for having what he calls "a rationale." There is none to propel him into the race, he says. And, as Martin Steadman, who until recently was his chief spokesman, observes, "He has a fierce pride in his credibility." The combative Cuomo who drives reporters batty by splitting hairs over the meaning of words is not about to surrender to the charge of hypocrisy.

A Cuomo rationale won't materialize unless all of the current candidates fall flat. This probably can't occur until after the first tier of caucuses and primaries in early 1988, or at least until March 8 -- Super Tuesday in the South. By then, the arithmetic doesn't add up for Cuomo. Forty percent of the Democratic delegates already will have been selected by March 8, and filing deadlines for candidates to get their name on the ballot will have passed in all but 11 states (representing only 9.78 percent of all the delegates), according to James Carey, executive director of the Democratic National Committee's Compliance Assistance Commission. Even if one assumed (wrongly) that Cuomo could garner all of the 640 at-large super-delegates (National Committee members, governors and members of Congress), these constitute only 15 percent of the 4,160 delegates.

But . . . . Cuomo does open the door a crack, admitting he has occasional second thoughts. "I'm going to keep my life very simple," he says while riding in the front seat of his state car, a grey wool hat pulled over his ears, after leading a state Democratic committee luncheon forum at which Rep. Patricia Schroeder, who is considering running, appeared. Referring to his decision of last February not to run, Cuomo says, "I make crisp decisions. And then I question myself all afternoon."

Was this just Cuomo the introspective brooder talking? Or was this a man with real regrets? If Cuomo has a clandestine presidential strategy, it can work only if he avoids leaks. By definition, therefore, his true plans are known only to himself.

This much seems certain: The only plausible Cuomo scenario is one that takes place at the convention. Should his party deadlock because none of the eight contenders enter the convention next summer with a majority and Democrats begin to clamor for Cuomo, then he is handed a rationale. "The only way he'd probably go in is if there's a deadlocked convention," says the man who is probably Cuomo's closest friend, New York Special Counsel Fabian Palamino.

If that were Cuomo's secret strategy, he would be free to spend the next year schooling himself -- out of the glare of primaries and incessant press queries. But this is a passive, prayerful strategy, one that waits for others to fail.

Cuomo seems honestly to believe that won't happen. So he looks relaxed. "The campaign for governor is over," says his son and political advisor, Andrew Cuomo. "The pressure of constant questions about the presidency is over. He's had a good year as governor." The snarl that accompanied his 1986 re-election is gone. With equanimity, he deflects questions that sprang from his cranky performance in that race -- including the concern, expressed by Washington political analyst William Schneider, that Cuomo is "thin-skinned" and perhaps "insecure."

"In terms of security, I have no need to know anything more about myself," says Cuomo. "I'm an 82. I'm never going to be a 90. . . I don't make the error of taking public approval or rejection as a measure of my worth."

The crash course Cuomo has undergone in preparation for his first visit to the Soviet Union has lured him out of his cocoon, and now he more freely ventures opinions on international matters. Of those on the political right who worry that Cuomo would be as mushy in dealing with the Russians as a bowl of polenta (Cuomo's description of Walter Mondale in 1984), he says: "Their point of view, as far as I can tell, is this: 'The Russians are evil. Their system of government is evil. Our system of government is good. Good should not deal with evil. You protect yourself, eternally, against the evil. And, therefore, the only thing that they understand is power and a powerful defense that could destroy them if they tried anything . . . .

"It leaves me with this question: You mean for the next four years we should spend another $15 trillion? You mean there is no way to negotiate our way out of this mess? I'm not prepared to believe that. I'm prepared to accept that their authoritarian way of life is not as good as our democratic way of life, that they have been guilty of human rights violations by our standards. And still are . . . . I think the conservatives lack subtlety. And the presidency of President Reagan indicates that. They want to cut taxes, they cut them too deep. They want to spend on defense, they spend too much. They want to balance the budget, they try to do it in three years. They overdo everything. I think life is more complex, more subtle. And that's the basic difference."

One area that Cuomo is not relaxed about is the whispering campaign about his family. "If you're Italian and run for president or vice president, the press looks into organized crime," says Schneider. "If a Jew ever ran, they would look for communists in the family. If an Irishman runs, they look for drinking." The whispers about Cuomo's aging and gravely ill father-in-law being an arsonist seem ludicrous, yet they persist. As do other tales. A week ago a woman in Anaheim, Calif., stopped Cuomo and said, he recalls: "I think you're great. Why aren't you running for president?"

Not interested, Cuomo told her. To which she replied: "Look, if your son is involved with the Mafia, that's not you!"

Cuomo was tongue-tied, and says he plans some day soon to speak out about the innuendos that skunk his family. Meanwhile, this week he is in the Soviet Union. In October he will be visiting three more states. In December, Mexico. He is broadening himself.

Should his party one day offer him a rationale to run, it will probably be similar to the one Cuomo offered the Indiana Democratic Committee last July: "The American people will insist on competence. And it is already clear that our candidates will meet that test easily.

"But that will not be enough, either. . . Nor should it be. The president will not be selected only on the basis of a volume of clever position papers and an impressive resume. The American people apprehend the leadership qualities they want in a more basic way. Most of all, we want our leader to see broadly, and to understand deeply. We want our leader to provide something to believe in . . . . " Passion, as well as competence.

That's the Cuomo message, and it lurks in this formless presidential campaign like the woman in the dimly lit bar.

Ken Auletta is a New York Daily News columnist and the author of "Greed and Glory on Wall Street."