An apparent computer glitch has held up the nomination of Terrence C. Golden as chief of the General Services Administration.

Reliable administration sources said Golden's nomination was supposed to have been submitted last week, but the White House personnel office discovered it had forgotten one important little detail: a background check.

The office apparently checked a computer and determined that Golden, now assistant secretary of Treasury for administration, already held a presidential appointment that had required Senate confirmation and thus would have undergone the review. In fact, the job was not converted to one that required Senate confirmation until after Golden was appointed in 1983.

Last Tuesday, Golden met with acting GSA administrator Ray Kline, who has held that job for nearly a year, to discuss their transition. The next day, Kline said he was "absolutely relieved" that the long wait for a new nominee was over. But by week's end, Golden was in a sort of bureaucratic limbo, waiting for his background check to be completed.

Before joining Treasury, Golden was managing partner of the Trammell Crow Residential Co., a major U.S. home builder based in Dallas; president of Palmas Del Mar Co., a Puerto Rican resort; and planning manager of a real estate firm in West Germany. Politically, however, he is an unknown.

John F.W. Rogers, director of administration and management at the White House, said he has worked with Golden on several projects. "He's a real friendly, open kind of guy . . . . He knows his real estate." More than half of GSA's staff is involved with real estate issues.

Golden has refused to comment until his nomination is submitted.

Several GSA officials have met Golden before -- when Treasury tried to fight GSA's efforts to move more than 1,000 departmental employes from downtown Washington to Hyattsville. Supervisors of the divisions involved opposed the move and took their complaints to Golden and then-Treasury Secretary Donald T. Regan. Regan went so far as to ask the Justice Department last month to declare the provision in the Treasury-GSA appropriations bill unconstitutional. Last week, however, Treasury agreed to back down.

GSA Comptroller Ray A. Fontaine, who was involved in the dispute, said he "found Golden to be a good negotiator, but he was captured a little too much by his bureaucracy. They were telling him things that just weren't true."

Fontaine said he thought Golden was a lot like former administrator Gerald P. Carmen. "He Golden may be a little more naive but he's . . . had a little more finishing school than Carmen." ROADBLOCKS? . . .

GSA has told the Office of Management and Budget that there are six major "congressionally imposed impediments" that hinder GSA's ability to operate efficiently.

OMB has agreed to seek changes in two of them: streamlining the construction review process on Capitol Hill and eliminating barriers to the contracting out of certain GSA functions.

GSA's report to OMB said congressional review of construction and major repair projects has caused "delays, lost business opportunities and higher operating costs." GSA also said it opposes restrictions on contracting out that give a "preference to selected groups, such as veterans and sheltered workshops for the blind and severely handicapped, that result in less savings and reduce competition."

GSA would also like to be able to sell federal property without having to complete a review of the environmental impact; pay federal employes a set daily allowance when they travel, whether they actually spend it or not; end congressional review of the sale of surplus personal and real property; and eliminate the Davis-Bacon, Walsh-Healy and the Service Contract Acts -- and the restrictions they place on various kinds of federal contracts.