When Citibank Chairman Walter Wriston was asked how many dollars there are overseas, he said, "Nobody knows. It depends on how many times you count the dog when he runs by the door."

Although there is no definitive way of knowing just how many of those dollars, known as Eurodollars, are overseas and out of the hands of U.S. regulators, the number clearly is big. Estimates run as high as $750 billion, but that includes considerable double-counting when dollars change hands more than once.

In any case, the number of Eurodollars available has grown exponentially during the past two decades. If one accepts the $750 billion figure as legitimare for comparison purposes, then the comparable 1969 figure would be less than $100 billion. A decade before that, the Eurodollar virtually did not exist.

And now, for the first time, world bankers are expressing concern over the size of that market and the impact it can have on their own economies. A series of meetings among international banking officials is leading to the development of the first system to control this behemoth, with the distinct fear that if such action is not taken soon, the world monetary system will become too fragile, and many nations' economies could become vulnerable to politically induced money movements.

The advantage of borrowing a dollar from a bank outside of U.S. regulatory control is simple: It is a cheaper dollar to borrow. Various restrictions placed on dollars held by U.S. banks in this country serve to increase the cost of borrowing a dollar here by about a percentage point over the cost of borrowing a Eurodollar. The major reason for that difference is requirements that a certain percentage of a domestic bank's demand deposits -- in some cases more than 16 percent -- be kept frozen in the bank rather than lent out. Thus the domestic bank is saddled with the cost of holding on to money, while its overseas counterpart can loan out every cent it has, increasing its profits. Unless, of course, too many loans go bad.

The rapid growth in these uncontrolled dollars around the world has helped facilitate world trading immeasurably, enabling huge sums of money to be recycled endlessly, and be used to lubricate world commerce. When members of the Organization of Petroleum Exporting Countries deposit their billions of petrodollars (dollars earned as payment for oil shipments) in international banks, that money is redistributed almost immediately to willing borrowers.

But concern is growing that this mass of Eurodollars -- which exist only in the computers and on telexes of multinational banks and corporations -- is doing more than just helping along world trade.Critics say there are so many Eurodollars that they are fueling world inflation by making it too easy for companies and nations to borrow money. There is a reason for all those reserve requirements at home, these critics add, and that is to force bankers and borrowers to be more prudent, and to keep their monetary supply within safe bounds.

Other monetary experts downplay the warnings of worldwide inflation, and claim the banking industry and the world economic system can and do take care of themselves to a large extent.

"The scale of the Eurocurrency market (includes Eurodollars and other currencies floating outside of their countries of issue -- estimated to be another $250 billion) is often misunderstood," said Henry Wallich, a member of the U.S. Federal Reserve Board. After netting out various sums which he said are essentially duplicative, he set the "so-called stateless money" total at between $100 billion and $120 billion.

Still, "The importance of the market should not be underestimated," Wallich said. "The absolute numbers are large."

The fact world bankers have become more concerned over the past several months about the stability of the Euromarket and other world money markets. There have been calls in the U.S. Congress and the governing bodies of major European countries for new controls over the Euromarkets to control their growth.

And although the world banking community has taken it upon itself for some years to keep track of banks doing Eurocurrency business, it has been concerned only with making sure banks don't overextend themselves. Without the traditional domestic-type controls, banks doing considerable Eurocurrency business have to keep themselves in line, or risk the kind of overextension and collapse that caused a couple banks to go under a few years back.

Now the banking community has become convinced that the international money supply has grown to such proportions that it is having a direct impact on the various domestic monetary systems. When the Fed has taken anti-inflationary actions such as imposing credit limits, it has found that domestic banks merely go overseas and bring in Eurodollars.

"The larger the amount of offshore dollars, the larger a given domestic monetary policy action has to be in order to reach its objective," observed Anthony Solomon, undersecretary of the Treasury for monetary affairs.

And there is no reason to believe that the amount of offshore dollars will not continue to grow. "Every year we think the Eurodollar market won't grow anymore," said a top international money expert for one New York bank. "But it always does. I've just stopped predicting no growth. I do think, however, that without some of the actions we are taking, the growth would be much greater."

That banker is one of several world banking and government officials who have been meeting informally to develop new controls over the world markets.

Because most countries have different ideas about how to control their own currencies, the concept of worldwide reserve requirements is considered by that banker -- and by most experts -- to be "unworkable in practice, and maybe even unworkable in theory."

But the meetings among the central bankers have begun to bear fruit: a consensus to go to a consolidated-balance-sheet approach, which means the central banks of each country should keep track of their own banks, including their foreign branches. That way every branch of every bank will fall under some scrutiny.

And now several countries are heading toward imposing their own domestic controls, which eventually will affect the world markets. The United States only last month began requiring banks here -- including foreign banks with offices in the United States -- to keep 8 percent of any new borrowings from the Euromarket in reserve. That means they can lend out only 92 percent of the money they borrow from Euromarkets, making that borrowing more expensive. And only last week a Japanese newspaper reported that the Finance Ministry there is considering a series of measures to tighten foreign exchange controls in that nation.

More such actions are expected around the world. The United States and West Germany have been particularly active in jawboning other countries to impose reserve requirements on the various foreign currency deposits in their banks. These two countries have been particularly concerned because they have been the most vulnerable to Euromarket fluctuations.

"Given the enormous complexities of the problem, I think it will take some time to bear fruit," said Treasury's Solomon of the international talks going on. "But the discussions are continuing, and everyone is being cooperative. Still, it is going to be a long haul."

One of the problems world bankers are encountering is a worldwide mistrust on the part of political leaders. Opponents of the multinational banks, who call for strict controls, have seen their cause fueled by such events as the recent Citibank furor, in which a former overseas officer for that bank described a system he said the bank used to reduce its tax bite in many of the countries in which it operates. The system of parking profits from one overseas branch to another was so simple that it infuriated banking authorities in several of the countries where there is considerable banking activity. The lesson learned by many of those countries was simple: No matter what restrictive action any one country takes, a multinational bank can get around it.

Although the Citibank case centered primarily on incidents in Europe and Nassau, the Latin American countries have been upset the most, threatening to take much harder stands on banking practices in their countries. "We have leaned over backwards . . . in these countries so that we would not be regarded in the same light as the multinationals. Now attitudes seem to be hardening against us," one British banker told the Financial Times.

But bankers are notoriously slow to impose new restrictions on themselves. Despite the new rounds of talks, "There is little likelihood of further actions in the short term," said Solomon.