What, if anything, can or should be done about money market mutual funds? That's the question that increasingly preoccupies the banking community and its regulators.

The controversy, fueled by the 62 percent increase in the funds' assets since January -- to nearly $120 billion -- pits the funds against banks and savings and loans. Lined up on the side of the funds are their shareholders, who want to protect their investments, as well as some government officials who believe restraints on the funds are unnecessary, unwise or unworkable.

In the other side are aligned savings and loan associations, mutual savings banks and small commercial banks, which believe the money funds are rapidly draining away their deposits, as well as some legislators, who think curbs are desirable.

Somewhere in between are large banks and a few thrifts, which would like a chance to compete equally with the funds, as well as key legislators and the Federal Reserve, which has not yet taken policy stand. Most of these views are expected to be aired Wednesday and Thursday in hearings by the Senate Banking Committee and later by the House subcommittee on domestic monetary policy, chaired by D.C. Del. Walter Fauntroy.

At this time the legislative outlook is unpredictable. Yet, while the debate goes on, depository and other nonbanking institutions are devising their own ingenious ways of competing with money funds by setting up their own money market funds through subsidiaries or paying comparable rates on shortterm certificates.

The chief attraction of money market mutual funds is their ability to pay top dollar (currently the average yeild is 14.6 percent). To this should be added their complete liquidity, good safety record for preservation of capital, low minimum initial deposit and, to a lesser extent, their third-party payment checks.

The funds, whose high-grade investments are in short-term government securities, commerical paper and certificates of deposit, can offer shareholders attractive terms because they are not constrained by banking laws, although they are subject to securities regulations. They do not make loans and therefore incur no losses; they are not required to set aside reserves on checking accounts against possible losses.

In practice the value of the shares remains at $1 whereas the yield vacillates, thus giving the customer the impression of having a fixed deposit. The principal of the account is not insured, however.

No reliable statistics exist to demonstrate just how much money is flowing from savings accounts to money funds. A survey commissioned last year by the American Bankers Association reported that 56 percent of those questioned named savings as the source. There was no attempt to translate this into dollars.

During the first quarter, savings and loans and mutual savings banks witnessed a net outflow of $2.85 billion in deposits. They assume without documented proof that most of this is going into money funds. An informal telephone poll of local shareholders conducted by Fauntroy's domestic monetary policy panel showed half of them had shifted money from their checking and savings accounts. Again, there were no dollar figures.

The Investment Company Institute, the trade association of mutual funds, does not address directly the question of the source of its money except to say that about $12 billion is in accounts of under $10,000. These are the funds that would earn the minimum 5 1/4 or 5 1/2 percent passbook rate. The ICI contends they represent but a drop compared to the ocean of $1.4 trillion now held in banks and thrift accounts.

There has been no attempt to measure how much money in certificate of deposit was withdrawn and placed in higher-yielding money funds. Individual funds have initiated letter-writing campaigns by their shareholders to block any restrictions. About 300,000 letters have been received by congressmen.

The thrifts' real problem is high interest rates, which reduce the spread, or profit, between their portofolios of low-interest loans and the high rates they now must pay on about 70 percent of their funds derived from deposits and loans. The ICI analysis is shared by the Reagan administration. Imposing curbs on money funds would be, according to Treasury Secretary Donald T. Reagan, "the wrong approach to assisting the thrift industry." He said curbs would accelerate the growth of other high-rate investments, such as Treasury securities, and would raise a cry for more restrictions.

The Fed, however, hadn't decided as of last week whether any action should be taken. Fed governors don't favor additional regulation. Yet some have expressed concern that money market fund transaction accounts are not counted along with other checking accounts, a fact that makes it more difficult for the Fed to get a grasp on the money supply.

This is also the primary concern of Fauntroy's banking subcommittee. Of the six bills already introduced in the House (none thus far in the Senate) to curb money funds, Fauntroy's is the most comprehensive. fIt would allow the Fed to put reserve requirements on transaction accounts. The provision that most arouses the ire of the money funds directs the Depository Institutions Deregulation Committee to "establish the maximum rate of return which is payable on funds invested in a money market mutual fund." In the words of David Silver, president of ICI, this means the regulators could reduce money market rates to "5 1/2 percent plus a toaster."

Subcommittee staff member Howard Lee insists this is a misreading of the bill's intent and says that the language will be rephrased.

Fauntroy, like Sen. Jake Garn (R-Utah), chairman of the Senate Banking Committee, has said he favors putting reserve requirements only on the checking portion of money market accounts. The practical effect of such an action would be to split money funds into two types, those with checking privileges and those without. Those with checking privileges would yield anywhere from 0.5 to 1.5 percentage points less.

ICI's Silver refused to comment on such a compromise at this point, saying that the Fed would first have to decide whether reserve requirements are necessary on money fund transaction accounts. In his opinion, the small amount of activity -- an average of two checks a year written on each account -- doesn't warrant reserves. But if the Fed decides it does, "then we would engage in rational discussion," he said.