The Federal National Mortgage Association, in an effort to find new sources of mortgage money, is seeking Treasury permission to activate an offshore financing subsidiary.

Foreign capital represents "a new source of funds that we should be tapping, and we're eager to develop its potential," Fannie Mae chairman David O. Maxwell said last week.

There are "investors outside the United States with billions of dollars in surplus capital to invest," Maxwell said, and their money "could prove to be one of the most potent tools in our efforts to provide adequate funds for housing in the future."

This is not the first time Fannie Mae has cast a longing eye toward foreign capital markets. In 1974, it set up FNM Overseas Capital Corp. in the Netherlands Antilles but never activated it.

Now, however, the question has taken on a new importance. With the deregulation of banking and with interest rates likely to continue to bounce up and down, most experts in the field agree that few mortgage lenders will be willing or able to make long-term loans and hold them in their portfolios.

Instead, lenders will be looking to make loans and then sell them in the so-called secondary mortgage market to investors who find long-term yields of 11 percent or so (at current rates) attractive.

Critical to this, and thus to the availability of mortgages, is the assurance to lenders that there will be enough money in this secondary market to buy up the loans they write.

Pension funds are often mentioned as a potential source of much secondary mortgage investment money. But the demand for mortgage money is so large--figures in excess of $1 trillion have been cited for the remainder of the 1980s--that pension funds plainly cannot supply all of it.

Maxwell, speaking to the U.S. League of Savings Institutions' Secondary Mortgage Market Conference in Miami, expressed optimism that foreign money could fill much of this gap. Outlining "the dimensions of this opportunity," he noted that "from 1978 to 1982 total foreign investment in the United States more than doubled to $130 billion. . . . The Eurodollar bond market, bonds issued in dollars abroad, also shows enormous growth. Its volume has tripled in the last three years. . . .

"But what is appealing about these markets," he added, "is not just the amount of potential capital they promise, but the reasons foreign investors have for seeking U.S. securities. We believe there is real compatibility between what they are seeking and what the secondary mortgage market has to offer."

If the Treasury approves activation of its Netherlands Antilles subsidiary, Fannie Mae "will launch a major marketing campaign to make foreign investors aware of the attractions of our U.S. home mortgage market . . . ," Maxwell said.

The Netherlands Antilles subsidiary is the key to foreign investment because its tax treaty with the United States allows interest paid to investors there to escape a heavy U.S. withholding tax that would otherwise be imposed.

The issue is a thorny one for the Treasury, which is in the process of trying to renegotiate the treaty so as to close the Netherlands Antilles "window."

Asked about the status of Fannie Mae's request this week, a Treasury spokesman would say only that his agency has not responded. He refused further comment, citing the "sensitive treaty negotiations" that are going on.

The issue has also proved sensitive on Capitol Hill. When the late Rep. Benjamin S. Rosenthal (D-N.Y.) discovered FNM Overseas Capital in 1980, he accused Fannie Mae of seeking to help foreign investors escape U.S. taxes.

Rosenthal's consumer and monetary affairs subcommittee, now chaired by Rep. Doug Barnard Jr. (D-Ga.), is currently investigating "the misuse of offshore tax havens, specifically, the Netherlands Antilles, for tax evasion purposes," according to a panel staffer.

The staffer said the panel has evidence of "large purchases" of Eurodollar bonds by U.S. citizens through the Antilles to escape taxes. He noted that heretofore much of the debt issued through the islands has been coupon bonds, which has made the payment recipients very hard to keep track of.

He said that if Fannie Mae gets the Treasury go-ahead, the subcommittee would be "very interested how the debt is issued" and in "what kinds of protections" the association plans to make sure proper taxes are paid.

Fannie Mae spokeswoman Beth Van Houten said the association would "certainly comply with Treasury or IRS requirements" but is "not going to do any more or any less" than other issuers of debt through the Antilles.

Sources said, however, that Fannie Mae's proposed borrowing, which is expected to be in the $200 million to $300 million range, would be issued in bearer form, raising, as a Barnard subcommittee staffer put it, the specter of Americans using the notes to avoid taxes.

To Fannie Mae, the central issue is fairness. Arthur P. Solomon, the association's executive vice president and chief financial officer, noted this week that "numerous corporations have taken advantage of this form of financing and we think we're being treated unfairly."

"In 1982, there was approximately the same amount of borrowing by U.S. corporations in the Eurodollar market as there was in the U.S.," he said, but "housing has been literally shut out."

In his speech, Maxwell said, "We're not asking for special treatment, just equal treatment. We believe that housing deserves parity with other business purposes for it is surely as important to our economy and to our people. . . . "

"Moreover," he said, "our success in tapping offshore capital could relieve strains in the domestic credit market and thus help move domestic interest rates downward."