The nation's savings institutions proposed a plan this week designed to triple the reserves of the debilitated Federal Savings and Loan Insurance Corp. without further damaging their own precarious financial condition.

The FSLIC fund, which insures about $800 billion in deposits, has fallen below $6 billion, a historic low. Thus, it has 77 cents to cover every $100 of deposits. The industry plan, which would add $9.5 billion to FSLIC reserves, would boost that ratio to 1.98 percent, or almost $2 per $100 of deposits.

The U.S. League of Savings Institutions submitted the plan to the Federal Home Loan Bank Board on Thursday as an alternative to proposals made by the regulatory agency. Last December, the board said it was considering an additional assessment one-eighth of 1 percent of liabilities that would effectively raise the thrifts' current insurance premiums of $633 million annually by up to 150 percent.

Additionally, industry sources have reported that the board has suggested that thrifts make a $10 billion loan to FSLIC as well. A board spokesman declined comment except to say that a number of options were being considered and no decision had been made.

Rather than subject thrifts to the possibility of large premium increases for several years that would diminish their net worth, the trade organization devised a long-term plan to contribute 1 percent of each institution's liabilities, or some $9.5 billion, in return for preferred stock. The contribution thus would remain on the thrifts' books as assets instead of draining their capital.

The institutions would be eligible to receive dividends from the FSLIC, or regular insurance premiums would be waived if the net worth-to-assets ratio remained above 1.25 percent.

The funds also would enhance the FSLIC's reserves, whereas a loan could be used just to meet expenses, according to league economist Brian Smith. Increased reserves would enable the FSLIC to give more assistance to troubled thrifts in the future.

Credit unions were successful in similar legislation passed last year.