The Federal Reserve Board, responding to recent signs that the economy is about to enter a period of very weak growth, will probably act soon to loosen credit slightly so that interest rates continue to fall, according to sources knowledgeable about the Fed's plans.

Interest rates have been dropping since midweek, and a credit-easing move by the Fed should help keep borrowing costs down and sustain the economic expansion by making it easier for consumers and businesses to finance purchases of homes, appliances, equipment and other goods.

Lower interest rates also would be a welcome development politically for the Reagan administration, which has grown increasingly anxious about the election-year economy. But the Fed's action is unlikely to keep the economy from softening significantly in months ahead.

The disclosure about the Fed's intentions comes after a government report Wednesday raised fears that the United States will dip dangerously close to recession in early 1988. The report showed that businesses have been building heavy inventories of unsold goods, which could push them to cut production and payrolls.

The Fed wants "to make sure this is a slowdown and not a deterioration" in the expansion, a government official said. As a result, the Fed is "more poised toward ease than before," the official said, although any move to bring down interest rates will be limited because the central bank believes recession worries are overblown.

The Fed influences interest rates by controlling the supply of money to the banking system, but the level of most rates is determined by other factors as well, including banks' and investors' expectations about inflation and the demand for loans.

Mortgage rates, for example, already have been moving down to the 10 percent level in recent days, and yesterday the Veterans Administration, citing market conditions, reduced to 9.5 percent the maximum interest rate on home loans it will insure.

Administration officials have been prodding the Fed to ease for some time. They have refrained from publicly criticizing the central bank, however, for fear of appearing to pressure the new Fed chairman, Alan Greenspan, near an election.

One of the most ardent advocates of an easier monetary policy has been Beryl W. Sprinkel, chairman of the Council of Economic Advisers. Administration sources said Sprinkel complained that the Fed was draining too much of the money it had poured into the banking system in the wake of the Oct. 19 stock market crash.

For weeks, the Fed maintained a steady grip on credit, unconvinced by Sprinkel's argument that a slump could occur if the money supply continued to grow slowly. Fed officials saw little evidence that the expansion was at risk, and they wanted to minimize the chances of a renewed slide in the dollar. The dollar tends to weaken when U.S. interest rates fall relative to rates in other countries.

But in recent days, interest rates have declined in Japan and Europe, giving the Fed more room to ease. And Fed officials became more convinced that lower rates in the United States might help when the Commerce Department announced Wednesday that U.S. economic output had expanded at a brisk 4.2 percent pace in the fourth quarter of 1987.

Although seemingly good news, the report showed that the economy's growth was attributable mainly to a huge buildup in inventories, while consumer spending fell. Some economists said the development increased the odds of a recession this year.

Still, the Fed won't react to the new figures by trying to drive interest rates down sharply, sources said. The central bank probably will ease very gently, they said, because policy makers see a low probability that the economic slowdown will turn into something worse. Fed officials believe that an aggressive loosening of credit would bring unacceptable risks of inflation and a fall in the dollar.

In anticipation of an easier Fed policy, interest rates began to slide on Wednesday after the Commerce Department announcement. Yields on 30-year Treasury bonds fell to the 8.5 percent range as bond prices, which move inversely to interest rates, surged. The Treasury's long-term bonds had yielded 9 1/8 percent two weeks earlier.

Yesterday, yields dipped again, partly because of a story in the Wall Street Journal citing "signals from the Federal Reserve" that the central bank "may soon ease its grip on credit." The yield on the 30-year Treasury issue fell to 8.42 percent.