The Marriott Corp. yesterday offered to purchase the Saga Corp., a Menlo Park, Calif., food services corporation, for $425 million.

If Marriott successfully completes the purchase of Saga, which has $1.3 billion in annual sales, the Bethesda corporation will become the Washington-area's largest company.

Martin Marietta Corp., a leading aerospace company, presently leads the area in sales.

A spokesman for Marriott said last night that the offer was unsolicited and that the company requested a response from Saga's board of directors by 5 p.m. Monday.

Marriott offered $34 a share for all of Saga's approximately 12.5 million shares of common stock outstanding. That is $4.50 a share more than Saga's $29.50-a-share closing price yesterday on the New York Stock Exchange, where 128,700 shares were traded.

Marriott, with 1985 revenue of $4.2 billion that was up 20 percent from the previous year, operates Marriott hotels and food services, including Roy Rogers and Big Boy restaurants.

Saga Corp. sales of $1.34 billion last year were up 12 percent from 1984. Saga owns and operates restaurants and food service businesses, including Stuart Anderson's Black Angus Cattle Co., The Velvet Turtle, Hotel Foodservices and Spectrum Foods. It also owns and franchises the Grandy's, Straw Hat Pizza and Spoons Restaurant chains.

A part of Saga's business complements Marriott's high-volume food service to airlines and corporations. Saga provides similar services to corporations, colleges and hospitals in the United States and Canada.

Goldman Sachs & Co., Saga's financial adviser, has been retained to assist the board in evaluating the Marriott offer and possible alternatives, according to the company.

Saga said the company's board of directors will consider the Marriott offer at its regularly scheduled meeting on Friday.

Marriott's stock closed yesterday at $168.50 a share, down $4 on volume of 64,700.

J. W. Marriott Jr., president and chairman of the company, announced at Marriott's annual meeting last week that the board of directors had approved a five-for-one split of Marriott's common stock payable June 20 to stock holders of record on May 19.

Marriott's stock has taken a dramatic leap this year. Analysts say the run up is a result of investors' belief that the company will benefit from domestic tourism this year as vacationers stay home rather than travel abroad.

Marriott's 20 percent increase in profits over the previous year also speaks well for the company's management and continued growth, analysts said.

Saga Corp.'s 1985 profits were $22.5 million, down 34 percent from 1984, which the company attributed to high marketing, promotion and expansion expenses.