Dr. Earl Brian, the head of an investment group that is now in charge of United Press International, is an old friend of Attorney General Edwin Meese III and also is a principal stockholder in a company that last fall won a $40 million Justice Department contract.

A medical doctor who was California's secretary of health and welfare during President Reagan's governorship, Brian was involved in an investigation of Meese in 1984 while Meese's nomination for attorney general was pending before the Senate Judiciary Committee.

The inquiry, conducted by independent counsel Jacob A. Stein, found no basis for bringing any charges against Meese. Brian told UPI that he was later cleared in a separate investigation by the Securities and Exchange Commission, which conducted its own inquiry into possible insider-trading in the case.

Brian said in a telephone interview that although he may have seen Meese at large social functions, "I don't have much contact with him any more. Once the Stein thing came up, the contacts dropped off to nothing."

He said that even with the Justice Department contract held by one of his firms, the new managers of UPI are "under strict instructions to maintain its editorial independence" in its coverage of the department, Meese and the rest of the government.

Brian is chairman of Infotechnology Inc., also known as Infotech, a New York holding company that, according to SEC filings, counts nine information technology companies under its "control and influence."

Financial News Network, a 24-hour cable television service providing stock prices, is one of these.

Another is Hadron Inc., which last October announced that it had been awarded a $40 million-plus contract to supply computerized legal support services to the Justice Department's Land and Natural Resources Division.

Awarded after competitive bidding, the contract was essentially a continuation of a 1983 contract for computerization of legal data.

Brian said he owns 4 percent of Hadron and Infotech owns another 4 percent. Brian and three other Infotech representatives sit on Hadron's six-member board.

However, he said he was unfamiliar with details of the Justice Department contract, which was awarded to a wholly owned subsidiary of Hadron known as Acumenics Research and Technology Inc.

"It is not something that would come up to the Hadron board level," Brian said.

In the 1984 inquiry, Stein investigated whether Meese and his wife might have engaged in insider trading when Ursula Meese bought shares of Biotech Capital Corp. and American Cytogenetics Inc.

Until last September, Infotech operated under the name Biotech Capital.

At the suggestion of Ed Thomas, a friend of the Meeses and of Brian, Ursula Meese borrowed $15,000 from Thomas in January of 1981 and used the proceeds to buy 2,000 shares of Biotech Capital.

In the spring of 1981, again at Thomas' suggestion, she bought 200 shares of American Cytogenetics, according to the Stein report.

The report said that in the fall of 1981, Biotech bought a substantial portion of American Cytogenetics.

In 1982, Brian was supported by Meese and Thomas, who was Reagan's former Cabinet secretary in California and an aide to Meese at the White House, for a prestigious post on the National Science Board.

But Brian withdrew his name from consideration after the FBI conducted a routine background check, United Press International reported yesterday.

Brian told UPI that he withdrew his name because of "a hassle" with one of the members of the selection panel who had a rival nominee and that "nothing like {the FBI check} had anything to do with my decision at the time."