A federal audit is expected to show dramatic deterioration in the fund that insures deposits at U.S. savings and loans despite government efforts to stablize the industry, The Washington Post reported this week.

The Federal Savings and Loan Insurance Corp. faced liabilities of about $13 billion more than its assets at the end of last year, unidentified government sources told the newspaper, and that 1987 figure was more than double the $6.3 billion deficit at the end of 1986.The FSLIC insures deposits of up to $100,000 and manages failed thrifts. The Post said the fund's burgeoning deficit reflects deepening problems of the savings and loan industry, which has hundreds of insolvent institutions open because the government cannot afford to close them and pay off depositors.

Government estimates indicate the FSLIC deficit could grow in the next few years between $30 billion and $65 billion. Federal officials told the Post the government will squeeze healthy institutions to pay as much a possible on the deficit but taxpayer dollars also are likely to be used.

Reagan administration officials reportedly are alarmed at the rapid increase in the fund's deficit and the threat it poses to the U.S. financial system.

The White House Office of Management and Budget has joined other government agencies in looking at drastic measures to bolster the FSLIC funds, the Post said. Such steps would not solve all the problems but would ensure the federal government "had overturned every stone possible" to find money for the fund before seeking taxpayer help, one government official told the newspaper.

One plan under consideration, the Post said, would liquidate the Federal Home Loan Mortgage Corp., created by Congress in 1970 to funnel money from investors to home buyers. It employs 2,000 people across the United States.

The administration also is considering a merger of the FSLIC with the healthier Federal Deposit Insurance Corp., which insures deposits at commercial banks, the Post said. The FDIC has $18 billion in reserves.