In a move that may mean the Soviet Union is running low on cash, the Moscow government has begun financing its purchases of grain in this country with short-term loans from U.S. commercial banks, trade sources reported yesterday.

The reliance on credit in its grain dealings is an unusual development, since the Soviet Union usually pays cash.

Officials here believe that the quest for bank financing for these deals means the Soviet Union is undergoing a temporary liquidity problem brought on by falling hard-currency earnings from the sale of oil, gold and diamonds.

Soviet oil exports to the West in 1982 had been estimated at $14 billion, or about half its total foreign-exchange earnings. But experts now predict that these revenues could drop by as much as $3 billion as a result of the collapse of world oil prices.

Gold and diamond prices are also depressed, and as a result Soviet financial operatives have had to sell large volumes of these commodities at bargain prices to raise money for grain.

Western analysts cautioned yesterday against comparing the Soviet debt situation with that of its East European allies, several of which are facing severe difficulties in repaying loans. They noted that Moscow's overall debt to western commercial banks of $15 billion is easily manageable, given Russia's vast mineral resources and the size of its economy.

For example, the Soviet Union registered a trade surplus with the West of $1.5 billion in the third quarter of 1981, the latest for which statistics are available. Soviet deposits in western banks rose from $3.6 billion to $5.5 billion in the same period.

Nevertheless, U.S. officials and grain traders said these positive developments are now being offset by a need to import sizable quantities of grain. On March 4, the Russians bought 600,000 tons of U.S. corn, bringing total purchases of U.S. grain from the 1981 crop to 6.8 million tons of corn and 5.9 million tons of wheat.

This week's newsletter from the Washington-based U.S. Feed Grains Council reported that "indications have grown stronger that the Soviets are experiencing cash flow difficulties."

Officials at the Department of Agriculture said they learned for the first time two weeks ago that the Russians were seeking commercial credits to cover purchases. In 1972, the department's bank, the Commodity Credit Corp., extended a $500 million line of credit to the Soviets to buy grain. That U.S. government credit was not renewed, and Moscow's representatives moved to a straight cash basis in their U.S. transactions.

In another development, the Australian Wheat Board was reported to have approved a credit package that allows the Russians to finance one million tons of wheat purchased in that country.

Grain trade sources said the next clue as to the seriousness of the Soviet liquidity problems could come when Moscow places its orders for the 1982 Argentine grain crop, which will be harvested over the next few weeks.

In 1981, the Soviets bought almost the entire Argentine grain surplus. Sales to the Russians accounted for 14.9 million tons out of the total 16.9 million tons of Argentine wheat, corn and sorghum shipped abroad by the private grain trade. Sources said that these purchases, like those in the United States, were paid for with cash.