Fairchild Industries Inc. is optimistic that it will make the first overseas sale of its A-10 close support combat plane to South Korea some time this year, two top company officials said today. The Montgomery County aerospace firm also reported a sharp increase in profits.

"It (the sale) seems to be getting closer than ever," said Fairchild president John F. Dealy in an interview after the company's annual stockholders' meeting here, at Fairchild's Republic Division.

Dealy and Republic president Robert J. Dixon, a retired Air Force general, said in separate interviews that Fairchild executives and South Korean government officials are holding continung talks about an A-10 purchase. Neither man would say how many of the airplanes-costing $5 million each-the South Koreans are thinking of buying.

Dealy and Dixon said, however, that the South Koreans are considering purchasing either the A-10 or additional F-5 fighters manufactured by Northrop Corp., of Los Angeles. South Korea, like many other foreign governments, already has F-5 fighters.

Fairchild's Republic Division has been making the single-seat, twin-engine turbo prop A-10 since 1973, when it won an $800 million U.S.Air force contract following a stiff flyoff competition with the Northrop Corp. Fairchild makes most of the parts for the A-10 at Republic in Farmingdale, but assembles the plane in Hagerstown, Md. The Air Force wants to buy 733 A-10s by 1982, pending congressional approval. So far, 339 A-10s are under firm contract and the company has delivered 165 planes to the government.

Company officials said the A-10 has been primarily responsible for lifting the Republic Division from a financial slump. Six years ago the company, once among the nation's major producers of fighter planes, was down to a work force of only about 1,700. Now, Republican employs about 6,000 workers and was rated by the Pentagon last years as the nation's 2ind largest defense contractor.

Dixon, who became Republic's president last September, said of the A-10-sale to South Korea: "They're interested. The Koreans have visited here (Republic at Farmingdale) and we've gone there." He said discussions have been ongoing for serveral years. Dealy said the company "has an idea" of how many A-10s the South Koreans would buy but he declined to elaborate. A possible deal, he said, "seems to be getting closer" and might even come some time this year.

There were these other developments at the company's annual meeting:

The company disclosed that its space and electronics division in Germantown, Md., is now competing with TRW, an electronics firm, for an $80 million-to- $100 million National Aeronautics and Space Administration contract to build two satellites for NASA's international solar polar mission. The project, scheduled for 1983, is aimed at launching the two satellites at the sun to study radiation patterns. NASA is to award a contract Oct. 1. Dealy said the contract would mean an additional 20 jobs at the space and electronics division, which now employs about 700 workers. He said also, that if awarded the contract, the division would construct a sixth building at its Montgomery County site.

Dealy said that the company had discussions with officials at the Chinese Embassy in Washington about the possibility of China purchasing Fairchild's military and commercial airplanes. He said the meeting was held at Fairchild's request and took place several months ago after the U.S. and China normalized relations.

Fairchild announced first-quarter earnings of $7.6 million ($1.56 a share) on sales of $155 million compared with 1978 first-quarter earnings of $5.8 million ($1.22) on sales of $121 million.

Officials attributed the substantial gains to increased airplane deliveries by the Republic Division and by Swearingen Aviation Corp., of San Antonio. Swearingen was acquired by Fairchild in 1972 and manufactures and Merlin and Merlin commercial aircraft for business corporations. CAPTION: Picture, MAY I SPEAK? - Fairchild Industries President John F. Dealy raises his hand during yesterday's stockholders meeting in Farmingdale, N.Y. Secretary John D. Jackson is at the left, Executive Vice President Charles Collis is next and Chairman Edward G. Uhl is behind the lectern. Officials expressed optimism on plane sales. AP