MOSCOW, SEPT. 23 -- New York Gov. Mario Cuomo, on a whirlwind tour of the Soviet capital, has been working hard at not running for president.

In three days, he has been to see top Kremlin policy-makers and Nobel Peace Prize winner Andrei Sakharov, made stops at a synagogue and at the Moscow patriarchy of the Russian Orthodox Church, visited a housing project and sports complex, had dinner with a Jewish family refused permission to emigrate and lunched with the U.S. ambassador.

For those who are wondering what this grand tour has to do with Albany politics, the New York Democrat answers the question before it is even asked.

"I wouldn't do this because I was trying to get ready for a presidential bid," he said in an interview today. "There is no presidential bid for me. There never will be, because we will win in 1988, and the person who wins will be there for eight years. And eight years from now, no one will remember my name."

But Cuomo, who formally announced his noncandidacy in the 1988 race last February, is having a hard time convincing people of his nonintentions. Among the unpersuaded are his Soviet hosts who -- perhaps sensing a vacuum in the Democratic Party's presidential ranks -- have laid out the red carpet for the traveling governor, his staff of 10 and an accompanying entourage of 14 Albany-based reporters.

The large press corps -- which Cuomo says he tried to discourage from coming along -- has dogged his heels at every stop, recording statements that have revealed gaps in the New York politician's grasp of U.S.-Soviet issues.

After a meeting with Politburo member Vitaly Vorotnikov on Monday, Cuomo indicated his support for a Moscow proposal to hold a human rights conference here, unaware that Washington had responded negatively.

There were other stumbles as well. At one point, Cuomo praised glasnost, the Kremlin's policy of openness, telling Soviet dissidents that they could help their cause by not showing "disrespect to the government." But later he qualified his remarks, saying glasnost does not go far enough toward introducing democracy.

Before the trip, expectations that Cuomo would be received by Soviet party leader Mikhail Gorbachev ran high. Cuomo, here as a guest of the Russian Federated Republic, says he never asked for a meeting. In any case, Gorbachev is officially on vacation, amid unconfirmed rumors that he is ill or recovering, and Cuomo leaves Thursday morning for Leningrad without an appointment with the general secretary.

Cuomo said he raised the rumors of Gorbachev's illness at a meeting yesterday with senior foreign policy adviser Anatoliy Dobrynin and was told that the Soviet leader is well and resting in the Crimea.

While Cuomo professed not to be disappointed, he noted that several political leaders -- including former presidents Richard Nixon and Jimmy Carter -- assured him that Gorbachev would want a meeting.

"Everybody said he will want to talk to you -- not that you are important -- but you are a visiting politician, you are from New York State, and he wants to talk to Americans."

The self-styled nonimportance of Cuomo's trip here has been undercut by its scale.

The International Center for Development Policy in Washington paid for the trip.

It began with the idea of delivering a lecture here in May, and has expanded to a schedule that includes stops at major Soviet newspapers and foreign-policy institutes, as well as talks with Dobrynin and Vorotnikov, the Politburo member and party chief for the giant Russian republic.

Cuomo has been shown on Soviet television and, according to his press secretary, has been sought out by dozens of Soviet reporters.

Tonight, at a visit to Rosh Hashana services at the Moscow synagogue, the governor was besieged by onlookers who spread the word that the "mayor of New York" was in their midst. "So he's Jewish?" asked one elderly woman, as she eyed him admiringly. Told he was of Italian origin, she appeared to be even more impressed.

Cuomo told Jews at the synagogue that "you still pay a big price for being Jewish in Russia, but it's getting better."

The trip to Moscow is Cuomo's first foreign excursion -- not counting a trip to Rome in 1980, as lieutenant governor, on a presidential commission. Those who believe he still has national political ambitions view it as required grooming in the field of foreign affairs.

Cuomo, once widely quoted as saying he didn't know "Beirut from Buffalo," said he decided to make the trip once he realized nothing he could say would convince people he was not running for the presidency.

"I used to worry about that, which is why I didn't travel," he said.

Now he said he is considering invitations to Japan, Mexico, Israel and Ireland.

But why Moscow first? Because, Cuomo says, this is the natural place to address the issues of peace and security which concern him "as a citizen and as a governor."

Pursuing themes developed in a series of speeches given during the summer, Cuomo is calling for a "new realism" in superpower relations to break the Cold War cycle of arms spending, and promoting stability in an interdependent world.

When he put these ideas forward at a U.S.-Soviet gathering in Chatauqua, N.Y., last month, he was criticized for being unrealistic and avoiding any mention of Soviet policies on human rights and Afghanistan.

Cuomo defends the speech, which he described as a welcoming address given by the host governor. "My mother, who was never educated in any language, would know that when you welcome somebody to your home you don't start by telling them how dirty their daughter's face is," he said.

Cuomo's ideas found a receptive audience here. A Soviet specialist in U.S. affairs described him as "a politician who thinks, someone bigger than anyone else on the landscape."

"He has entered the field of foreign policy with some very refreshing thoughts and seems to be taking into account changes taking place here," said a Soviet who studies the American political scene.

Cuomo's reception is also a reflection of growing Soviet doubts about the chances for the current crop of Democratic candidates in the 1988 race, and bewilderment at the campaign's lack of focus.

"I don't recall seeing a situation that is so lacking in clarity," said one analyst.

For his part, Cuomo insisted he is developing his foreign policy expertise both to help his state and his party. "It helps me to speak for the Democratic Party on important issues," he said. "I will be speaking anyway, but now I know a little more about it."