American Finance System, Inc., a large consumer finance holding company based in Silver Spring, is engaged in preliminary discussions with "a large nationsl financial institution" about selling the company.

Senior vice president and treasurer Lee E. Alderdice announced the discussions in a statement that followed unusually heavy trading in AFS stock on the New York Stock Exchange yesterday morning - more than 44,000 shares exchanged hands before 11 a.m.

Trading in AFS was halted at $5.625, up 62.5 cents from Wednesday's close. The company subsequently said it was not "aware of any public information" to account for the stock market interest. ut Alderdice said AFS has had preliminary discussions with several different agents or principals regarding the availability of the company for sale.

"At the present time, initial discussions are being held with a large national financial institution, but no definitive understanding or agreement has been reached to date, nor is there any certainty that any understanding or agreement can be reached," he added.

Trading resumed later yesterday, and AFS closed at 5 3/4, up 3/4 on a volume of 69.200 shares.

Last summer, AFS indicated at its annual meeting that it no longer was seeking a merger partner - having failed to complete several proposed mergers since 1969 with other small-loan companies or financial institutions.

But AFS had emphasized that it would study any reasonable offers for the firm, which operates more than 400 small loan offices in 23 states. Founded in 1830, the local company has been rebounding from a difficult period during which it cut back some national operations and was forced to eliminate dividends.

Last November, AFS signed a $115 million credit agreement with 62 banks, with an initial maturity date of June 15, 1979.

In addition to its renewed profits growth (AFS earned $4.1 million in the first six months of 1977 compared with $1.2 million a year earlier), a prime attraction of the Silver Spring company for a national financial institution is its network of small-loan offices.

Looking toward the expected era of electronic fund transfers and financial transactions that transcend the traditional barriers to interstate banking created by branching laws, large American banking firms such as Bank-America are moving rapidly to establish nationwide consumer loan offices.

Citicorp of New York, for one, has been engaged in negotiations about expanding its business base in the mid-Atlantic states. AFS declined to identify the company with which it is talking.