American International Group, jockeying for a larger presence in the auto insurance marketplace, is considering an option to purchase a bigger stake in 20th Century Industries, of Woodland Hills, Calif.

20th Century may be looking into the prospect of selling the 58 percent stake of the company not currently owned by AIG to the New York insurer or another possible suitor.20th Century spokesman Ric Hill last week revealed little about his company's specific plans, ''I can't say one way or the other as to whether we are moving in that direction, and I am unaware of any other interested parties.''

New York investment banker Salomon Smith Barney Inc. has been authorized to examine strategic alternatives for upgrading shareholder value, according to a recent AIG federal securities filing.

A New York insurance analyst last Friday explained 20th Century's allure to AIG. ''AIG wants to be a much bigger player in the national direct written automobile insurance area, and 20th Century provides an excellent vehicle for obtaining that goal,'' said Michael Lewis, an analyst with SBC Warburg Dillon Read Inc.

''20th Century, originally a California direct auto writer, has expanded its operations into Arizona,'' Mr. Lewis said, ''and there could be further expansion into other states in the foreseeable future which fits in with AIG's national aspirations.''

Not all insurance analysts completely buy Mr. Lewis' assessment of the AIG-20th Century situation. Some insurance industry observers agree that AIG's existing position lets it gain direct-marketing capability that it wants, but they don't necessarily look for it to acquire the remaining slice of 20th Century.

20th Century generates nearly $1 billion in annual written premiums in California and Arizona. The insurer uses a direct response marketing program to attract customers, selling insurance through toll-free telephone lines.

AIG grabbed a 42 percent slice of 20th Century by investing $400 million in the company when it needed a capital infusion to ease its financial difficulties arising from more than $1 billion in homeowner insurance claims emanating from the January 1994 earthquake in Northridge, Calif.

The securities filing was made as AIG nears the February expiration of a standstill agreement that had kept it from increasing its stake in 20th Century. In that filing, AIG stated that it had informed 20th Century that it would be amenable to discussions about the prospect of purchasing the 58 percent share that the New York insurer doesn't have. AIG has expressed no interest in selling its current holdings in 20th Century to a third party.

AIG spokesman John Wooster, explaining the filing, said it was done to ''preserve our options for the future, but it doesn't in any way signal that we intend to do anything.''

Insurance analysts estimate 20th Century's value to be upward of $3 billion, but they have said that it could be difficult to divest itself of its remaining stake to a third party if AIG plans to retain its current position.

In its 1996 annual report, M.R. Greenberg, chairman and chief executive officer of AIG, said the company's personal lines strategy emphasizes multiple distribution channels, while focusing on cost efficiencies and the most advanced technology available.