Some time soon, President Reagan must make a critical decision: he must make up his mind whether to ask Paul A. Volcker to stay in office after his term as chairman of the Federal Reserve Board expires in August.

And if asked, Volcker will have to decide whether to accept.

Reagan has kept mum about his intentions. Publicly, he has said only--in response to press conference questions--that he hasn't had time to deal with the problem. Volcker has remained silent about his desires. He did once snap at an inquiring congressmen that he wasn't lobbying for the job.

There are many pressures within the administration working against a Volcker reappointment. Republican supply-siders, like New York Rep. Jack Kemp, urge the president to dump Volcker. Kemp wants Reagan to choose someone like Treasury Secretary Donald Regan who would apply a "standard" controlling monetary growth. "We don't have any measure to guide monetary policy now, just what I call a 'Volcker standard,'" Kemp said in an interview.

From Kemp's perspective, Volcker is undercutting a basic theme of Reaganomics by stressing the need to raise taxes as one way of cutting back the federal deficit.

From a strictly political viewpoint, what works against Volcker is that he is a nominal Democrat, appointed by Jimmy Carter (and it's not so much that Volcker is a Democrat as the Carter association). The Fed chairmanship, without question, is an appointment plum of as much enduring significance for any president as is the appointment of a chief justice. So, the president is urged, he should "name his own man"--and of course, a Republican.

Nonetheless, if there is any logic left in the world, Reagan, after a careful weighing of the pros and cons, will ask Volcker to stay on through the end of this presidential term, and for a short period after the new presidential term starts in 1985. Hard-core right-wingers might be appeased with other appointments--say to the Supreme Court, as vacancies arise.

Reagan and Volcker could agree on a plan by which Volcker stays, and they both support legislation that begins the term of the Fed chairman one year after a presidential inauguration. That would maintain the continuity of monetary policy now, yet give Reagan--if he runs and is reelected --or a succeeding president the chance to name his own chairman of the Fed.

If there is a modest economic recovery going this summer, the president may conclude that the worst thing he could do would be to depose Volcker. Uniquely, Volcker has the total confidence of the financial communities here and abroad, even when they don't totally agree with him.

His approval rating has gone up recently with evidence that the Fed is following a more flexible policy and has downgraded the more rigid monetarist approach of the first 18 months of the Reagan administration. This is the same flexibility that worries the more conservative among the Reaganites.

Volcker, who has reached the zenith of a career dedicated to the Federal Reserve and international monetary responsibilities "would find it hard to refuse" a presidential request to stay on the job, says one close to the scene of action.

He doesn't confide in his colleagues on this issue. There is a sense among many of them, nonetheless, that Volcker in a very human way wants to leave his powerful post of his own volition, and at a time when both the domestic and international economic crises have cooled down.

The one serious potential flaw in this otherwise logical scenario is that Volcker, who at some time must go back to private employment and earn enough money to make up for his poorly compensated years at the Fed, might well decide that this is the time to do it, while he is riding so high.

Reagan would then be faced with a serious problem. There is almost no one on the scene who could step comfortably into Volcker's shoes. First National City Bank Chairman Walter Wriston, a White House favorite, took himself out of the running. The financial markets' current first choice after Volcker is probably Alan Greenspan, former chairman of the Council of Economic Advisers. But even in the financial markets that Greenspan knows so well "there would be a testing period for him," says a Wall Street insider. Donald Regan has lost credibility in business circles because he has waffled back and forth on economic policy in the past two years.

And Fed Vice Chairman Preston Martin, a California Republican named to the board by Reagan early in 1982, viewed by some as a logical contender, is thought of as weak in financial markets and by many in the Federal Reserve system. History is also working against Martin: no vice chairman of the Fed has ever been appointed to the top job.