When Edwin Meese III, Reagan's right-hand man, was asked whether the president-elect expects Federal Reserve Chairman Paul A. Volcker to stay on, Meese was noncommittal. He wouldn't even say whether he thought Volcker had done a good job.

Meese's nonendorsement was in striking contrast to the assurance that Reagan wants William Webster, the present head of the FBI, to continue in office.

Volcker, to be sure, doesn't depend on Reagan's blessing: His term as chairman doesn't expire until 1983, and he has indicated no intention of getting out before that. But Meese's coolness is merely one of many indications that Reagan and the Federal Reserve may not be operating on the same wavelength. And circumstances could develop in which there could be a real confrontation testing the Fed's vaulted "independence."

First of all, Reagan is dedicated to the proposition that the economy is in desperate need of a large tax cut. It is the very centerpiece of his economic program, whether or not the tax cut eventually takes the full shape of the ambitious Kemp-Roth bill.

Volcker is reluctant to see big tax cuts without the more traditional approach of simultaneous budget cuts. In this, Volcker leans to the view of the Ford and Nixon "retreads" in the Reagan camp and away from the so-called "crazies."

More basically, there looms a fight over monetary policy. Reagan advisers -- from Milton Friedman on the monetarist right to middle-roaders like Murray Weidenbaum -- have been pointedly critical of the Fed for not sticking to its targets for controlled growth of the money supply.

Weidenbaum, an economist who served in the Nixon Treasury and who has been mentioned as a possible Economic Council chairman in the new administration, warned in a speech last week that "the stop-and-go monetary policy that has characterized 1980 will cast its shadow on 1981." He complained that the very slow growth in the money supply in the first half of this year was followed by "an almost meteoric rise," which presages another shift toward restraint. "Depending on the speed and intensity of the change, the fragile recovery may sputter or even abort," Weidenbaum said.

At this stage of the game, almost no one is happy with the Fed. Despite the introduction 13 months ago (with much fanfare) of new money management techniques, the Fed can't claim that it has a handle on either the money supply or on interest rates, which have skyrocketed again.

Salomon Bros. partner Henry Kaufman said the other day that he had "considerable doubt" that the Fed can accomplish its ultimate objective, which is to tame inflation. Given its performance as against its promises, Kaufman charges, the Fed no longer has "credibility in the real world."

Kaufman, who has an outstanding record for pinpointing the trouble spots, says that the Fed is now "veering toward both disarray and compromise in its monetary policy." The crux of the problem, he says, is that the Fed hasn't kept pace with all of the new kinds of credit that the private sector calls "money." Therefore, says Kaufman, the Fed is behind the times in trying to define "money," let alone control its supply.

At Fed headquarters on Constitution Avenue, there is a recognition that communications with the incoming Reagan administration may not be the best and that relations at the start may therefore not be too smooth. "There seems to be an illusion," sighs a top source, "that you can deal with inflation by keeping the money supply stable -- that somehow, that's all you have to do, and wage bargains will magically retreat from 10 percent to 2 percent a year."

To some extent, the "illusion" of which the Fed complains may arise from an esoteric debate on technical questions relating to Fed procedures. In part, as well, the Fed itself may be to blame for the simplistic notion that a stable growth of the monetary aggregates is the magic answer to inflation.

But what Fed policy makers stress now is that monetary targets will be useless in controlling inflation if they are not supported by other appropriate government policies, especially fiscal restraint. The Reagan crowd doesn't contest that, but argues that this is a cop-out -- that the huge federal deficit is no excuse for the erratic money supply fluctuations that the Fed countenanced in the past year, which they say caused uncertainty in financial markets and economic instability everywhere.

Some Reaganites grumble that they may have to wait to twist Volcker's arm: If the Fed doesn't shape up, they say, they'll ask Congress to set tighter targets that the Fed would be forced to follow. That would be resisted not only by the Fed, but by moderates on Reagan's side, who acknowledge that some sense of judgment, rather than a slavish devotion to monetarist theory, must guide the Fed.