ALBANY -- Mario Cuomo, governor of New York, wishes the press and public would take him at his word: he's not runningfor president. After a long interview in his office here -- focusing on economic issues -- I'm almost, but not fully, convinced that he means it. Only Cuomo knows what he's going to do.

But if anyone has done his homework better on our underlying economic and social problems, I haven't met him. For example, he volunteered an opinion on Treasury Secretary James Baker's involved and technical proposal for a commodities price index, including gold. (He likes the idea.)

''If I go to the Council on Foreign Relations and do well {in a speech on foreign policy}, they say: 'He's running.' If I don't, they'd say I don't know anything about foreign policy,'' the governor complains.

Cuomo is just as charismatic on the second floor of the state capitol as he was when he electrified the 1984 Democratic National Convention in San Francisco with his keynote address. He has a keen sense of what is going wrong in Washington. And if next year, when he is 56, circumstances tilt the Democratic nomination to someone else, the nation and his party are going to be listening to this man at age 60 or 64. He has too much raw energy to be denied.

In shirt-sleeves, his collar loosened, Cuomo rattles off the list of America's bitter economic problems, all interlinked and symbolized by the stock market crash: the budget deficit, the trade deficit, a declining dollar, Third World debt and a president all but stripped by events (many of his own doing) of remaining power.

The time has come to reduce the ''entitlement'' programs -- including Social Security -- for income groups that don't need them, Cuomo says. ''We've got to put everything on the table, except programs for the really poor.''

He would take a big bite out of defense, especially because ''Gorbachev finds himself in an extreme version'' of America's economic distress. ''If you don't recognize that,'' he says, addressing himself to the American body politic, ''then you're missing the great bargaining opportunity of the past 40 years.''

If this week's budget-reduction exercise fails, congressional Democrats and cooperating Republicans such as Majority Leader Robert Dole and Sen. Pete Domenici should take things in their own hands, forge a credible package, then confront the White House with it, Cuomo said. ''You've got to move now. The whole rest of the world is looking at us!''

Yet that would be only one small step on a longer road to recovering America's greatness, so far have we slipped behind other major nations, he believes. ''But you've got to be an optimist,'' he says with an evangelical zeal. ''This country is capable of miracles. With all of our problems, we have not begun to use our potential strength.

''Take our work force. Where will this country be when you do finally educate all those blacks and Hispanics {now being ignored}? You now have 23 million illiterates, and you're behind much of the world in education. You're uneducated and undereducated -- and still you're powerful. Imagine where you would be if you got rid of the 23 million illiterates, and had only 5 million!''

The demand, as he sees it, is for leadership: ''We don't have a political power in this country. Reagan is on his way out. The Democrats? We don't know who they are, who is going to win the presidential nomination.

''But when we fuse it, and make a strong bipartisan government, which has to happen after Reagan -- in fact before he leaves -- finally, we sit down with one voice and put our own plan together, our own ideas intact, and sit down with the rest of the world and start doing business with Gorbachev, start trading with the Chinese.

''My God! We haven't begun to consider the possibility of China -- we're doing nothing with them. We're doing nothing with the Soviet Union. We have a lot of conservatives who say, 'God forbid, you should ever do business with them, that's what they're waiting for to make you weak!'

''Maybe we have to be smart enough to do business with them without getting raped. What's the matter, must you assume that the United States of America is a dummy, that we're not smart enough to make a deal without making ourselves vulnerable?'' His own guiding standard is, ''in everything, reasonableness.'' His economic policies, he says, ''come very close to the center,'' because the center ''strikes me as being very close to the truth.''

Ideology, he holds, provides very few answers. On economic growth and full-employment goals, he wouldn't establish any fixed number, ''but be pragmatic and make it up as I go along.'' In seeking economic advisers, he doesn't look for an exponent of any particular school. ''I would select someone intuitive,'' he said, ''because you can't cerebrate your way. You've got to guess right a lot of the time.''