Government Employees Insurance Co.'s proposed new holding company will concentrate on starting new enterprises or buying existing businesses in closely related fields, Vice Chairman Paul Hanna said yesterday.

Plans for the holding company, to be called Geico Corp. were revealed last week in The Washington Post and approved yesterday by the auto insurance company's directors.

In an interview, Hanna said he hopes Geico stockholders will approve the transaction at a special meeting early in February, after which the new parent company could open for business in about 30 days. Regulatory agencies also must act on the porposal.

Hanna, who joined Geico's top management last July 1 after a 32-year career with Manufacturers Hanover Corp. of New York and its predecessor banking firms, will play a key role in identifying new businesses for the Geico holding company.

When he retired from Manufacturers Hanover, he was executive vice president in charge of bank-related subsidiaries that have helped propel growth of profits for the New York bank firms.

"There are cycles in the casualty business, and we want to fill in product lines that are not so vulnerable," Hanna said of Geico's plan. At the New York company, when interest rates were low and bank profits depressed, subsidiaries engaged in financing and other services that require borrowing were able to secure funds at lower rates and post higher earnings, Hanna explained.

In the new holding company, which Hanna hopes will follow the Manufacturers Hanover example, Geico Chairman John Byrne and Hanna will be the chief executives, aided by a small staff. The auto insurance firm will be operated as a wholly owned subsidiary after a merger to be accomplished on a tax-free basis to Geico stockholders.

Hanna said he already is studying some potential acquisitions and at least one new enterprise, although no actual negotiations are in progress. He described the following as financial services Gieco Corp. will consider: mutual funds (primarily money market and tax-exempts), the savings and loan industry, industrial banks (a Geico affiliate, Government Employees Financial Corp., owns the largest industrial bank in Colorado), mortgage banking, leasing and general insurance brokerage.

In addition, Geico Corp. will study a number of new insurance lines, including health coverage, annuities, workmen's compensation and reinsurance.

Hanna emphasized that many of the proposed new business lines could benefit from the same type of direct-mail marketing that Geico has used successfully for 40 years. He said Geico management "wants to invest as much capural as it can" in the auto insurance business and has "no thought" of de-emphasizing that operation which is expanding its homeowners lines.

Byrne said last week that a major factor behind plans for a holding company was a more rapid growth in capital than the auto insurer can absorb. New Geico insurance salts have been rising but not as fast as new capital has been accumulated in the firm's dramatic recovery from near-failure in 1976.