Two-and-a-half years ago, when Frederick Schultz, a Florida banker and conservative Democrat, was nominated to the Federal Reserve Board as a governor and its vice chairman, he asked then-chairman Arthur F. Burns to describe the most important attributes of a governor of the powerful American central bank.

Schultz received a classic bit of Burnsiana: "I would say," the great man opined, "common sense and good judgment." That may seem to be a platitude, but there has been no oversupply of these qualities in Washington, and as Schultz prepares to go back to Jacksonville, he would be reassured if President Reagan keeps the Burns standard in mind when naming his successor.

In the best of all worlds, in Schultz's view, the new governor would be a businessman or banker with experience in making "day-to-day decisions." And to assure some regional diversification, he would come from the South or Southwest.

The board has enough economists, Schultz said in an interview. And especially, it can do without someone who represents a particular economic theory or philosophy. Precisely the same view will be conveyed by Fed Chairman Paul A. Volcker when he meets with Reagan at the White House early in the coming week. But Reagan, while he will consider Volcker's preference for a businessman, hasn't ruled economists as a group out of the running.

For example, this column can report that Reagan offered the Schultz seat to White House assistant Martin Anderson, an economist long part of the Reagan inner circle. But Anderson told me that he has turned down the offer, and the president is now considering a list of "at least a dozen to 15," including economists and businessmen, for an appointment that has some obvious implications going far beyond a replacement for Schultz.

It is hardly a secret that Volcker and the rest of the Federal Reserve governors feel it would be a serious mistake if Reagan puts an ideological stamp on the Fed by nominating a prominent monetarist such as Treasury Undersecretary Beryl Sprinkel to the board. Sprinkel believes that inflation should be brought under control by rigid regulation of the money supply, without regard to the impact on interest rates.

The new vice chairman--if close to Reagan--would probably have an understanding that he will succeed Volcker as Fed chairman when the New Yorker's term expires in 1983. That would have been the case had Anderson taken the Schultz seat. (Volcker's term as governor could last until Jan. 31, 1992, but no one would expect him to step down from the chairmanship to become a mere member.)

Beyond that, Reagan's first appointment to the Fed is likely to be taken by jittery financial markets as a clue to whether the president will modify his monetary-fiscal policy mix in response to enormous pending budget deficits, topping $100 billion in each of the next three fiscal years. Appointment of a businessman or other person whom the markets could label "pragmatic," rather than ideological, would suggest that the administration is keeping its policy options open.

In the wake of the new anxiety over box-car-size budget deficits, the White House may want to provide some assurance of its commitment to traditional Republican views. Commenting on statements last week by two members of the Council of Economic Advisers downplaying the importance of budget deficits, Anderson observed tersely: "Deficits do matter."

"The board needs a better balance," Schultz said in a long, reflective conversation. "It would be a good idea to get a broad-based person with a sound understanding of financial markets, and I think that would be well-received in the country. We don't need adherence to any particular theory. After all, the Fed is not an economic research laboratory. It sets monetary policy for the country, and its actions affect peoples' lives every day."

Yet, it is clear that even if a businessman, banker or other nonmonetarist is appointed by the president, the seven-member board will continue on what Schultz calls "a pragmatic monetarist" line, so long as the administration runs big deficits and an easy fiscal policy. He approvingly quotes his fellow governor, Republican Henry Wallich, to the effect that "inflation makes monetarists of us all."

Schultz believes that "the function of the central bank in this country has changed. Our goal used to be to promote growth consistent with price stability. But every time we had growth problems, we backed off the goal of price stability. Now, our goal should be only price stability, to get inflation down to a rate of 1 to 2 percent and keep it there."

How about the national goals of economic growth and reducing unemployment--can these be ignored? No, says Schultz, but these goals should be the object of the government's fiscal policy, while the central bank concentrates on price stability.

Having argued for the past year that a big tax cut leading to large deficits puts all of the anti-inflation burden on the Fed, there is no sympathy at the central bank for the sudden conversion of the president's Economic Council to the view that deficits are not necessarily inflationary.

Schultz last week testified before the Joint Economic Committee that Reagan needs "to do something" about the deficits, because "however you want to argue theoretically, the fact is that 99 percent of the people in this country believe that the deficit is causing inflation." So long as that is what people believe, he predicts, long-term interest rates will stay high, causing pain to interest-sensitive sectors like autos and housing.

What concerns the Fed, Schultz said in the interview, is that getting inflation under control by relying exclusively on control of the money supply "is the hard way, involving great risks, because it falls unevenly on specific sectors of the economy. Therefore, it subjects the government to great political pressures."

The difference between the Fed's and Sprinkel's approach is that the Fed, in Schultz's phrase, feels that "control of the money supply is necessary but not sufficient to control inflation," whereas the well-known Sprinkel formulation is that control of the money supply is the necessary and only tool needed to whip inflation.

As he prepares to leave Washington, Schultz fears that unless the Reagan administration modifies its policy mix, "interest rates will start moving back up again, although I do not think that we will see record high rates again. . . . The players in the markets see what happens with big deficits, over time. Either the Fed monetizes the deficits, which brings on inflation, or there is a firm money policy, leading to 'crowding out' and higher interest rates."