The Federal Home Loan Bank Board will consider allowing savings and loan associations to sell their old low-interest mortgages through a complex transaction providing tax shelters for investors, bank board chairman John H. Dalton said last week.

His proposal came as a surprise to the Department of the Treasury, which could lose considerable amounts of tax revenue if the suggestion becomes a reality.

The savings and loan industry is troubled by portofolios filled with low-yielding mortgages. If they were sold at current rates, the savings and loans would suffer huge financial losses, and the financial stability of some insitutions would be threatened.

The proposal Dalton discussed in a speech in Boston Friday would work this way:

A savings and loan would form a partnership with some investors, contributing old mortgages carrying low-interet rates. The investors would put up cash. The mortgages would be sold by the partnership at a loss, with the investors taking the loss as a deduction on their taxes. The S&Ls and loans would not suffer any losses.

Then the partnership would use its cash -- the money contributed by the investors and the proceeds from the sale of the old mortgages -- for new activities. It could offer new mortgages at current market rates, acting just like an S&L or bank or other lender. Any profits would be split between the savings and loan and the investors' group in the partnership.

The proposal would need legal approval from the Home Loan Bank Board and clearance for tax savings by the Internal Revenue Service.

The Home Loan Bank Board has not contacted the Treasury, parent department of the IRS, a Treasury spokesman said this week. "when we are contacted, we will study the idea," the spokesman said, adding no further comment.

Dalton said that the bank board staff is now prepared to accept formal applications from groups wishing to organize the partnerships involving S and Ls and investors. The applications will be considered "on a case by case basis ," he told the annual stockholders meeting of the Federal Home Loan Bank of Boston.

Approval by the three-member bank board itself would be required before any of the plans could be adopted by savings and loans. Dalton, the FHLLB chairman, is a democrat appointed by former President Carter. The incoming Republican chairman, Richard Pratt, has not commented on Dalton's idea. The third member is Andrew DiPrete, a Republican. Obviously, opposition by the Reagan administration could scuttle the plan in its infancy.

The savings and loans are anxious for assistance in handling their problem of low-yeild mortgages. Federally insured institutions have approximately $500 billion in mortgages, with $70 billion carrying interest rates below 8 percent.