Who will become the head of the General Services Administration when acting administrator Ray Kline retires next month?

The Reagan administration's choice for administrator, assistant treasury secretary Terrence C. Golden, remains in limbo, awaiting the completion of his background check, the submission of his nomination and Senate confirmation. All that is unlikely to occur by March 4, when Kline leaves for the National Academy of Public Administration.

Since Kline is also deputy administrator, the reins normally would be turned over to associate administrator Patricia Schoeni. But some senior officials say that's unlikely to happen because her agency experience primarily has been in personnel and administration rather than programs and because White House officials don't know her well.

Other names that have been mentioned include: William F. Sullivan, a former Veterans Administration official who took over this week as commissioner of the Public Buildings Service; Dwight Ink, a former deputy GSA administrator, and Donald C.J. Gray, now assistant administrator for the Office of Federal Supply and Services.

Among those who have expressed interest in the job are Lester L. Mitchell, who recently stepped down as Public Buildings Service commissioner; Charles S. (Terry) Davis III, associate GSA administrator for operations; William S. Bounds, the GSA's regional administrator in Denver, and Donald J. Layfield, the GSA's regional administrator in Atlanta.

Several bureaucrats say this is a particularly bad time for the GSA to be without a leader, because the agency is facing critical decisions on the fiscal 1985 and 1986 budgets. Kline, as it turned out, served a year as acting administrator when Jack Courtemanche's nomination ran into problems. ON THE FRONT BURNER . . . One of the hottest debates now raging at the agency involves the shape of the GSA's field structure. Options under discussion range from turning five of the GSA's 11 regional offices into district offices to a plan by three regional administrators that would save $86 million by abolishing many of the GSA's headquarters functions while strengthening field offices responsible for delivering services.

Some officials want to move quickly, to achieve greater savings and to meet goals set by the Office of Management and Budget. Comptroller Raymond A. Fontaine, for example, has said he plans to consolidate the agency's finance offices in the field.

But Davis, who is in charge of regional operations, apparently misunderstood the scope of what Fontaine had in mind. He fired off a nasty letter that said: "You should be aware that it does make morale a little difficult to sustain when regional employes find out from their . . . peers that their jobs are planned to be eliminated."

Jerald D. Fox, a senior aide to Kline, said no firm decisions, other than the one involving the finance offices, have been made. THEY'D RATHER FIGHT THAN SWITCH . . .

In 1982, Congress passed a law authorizing the Transportation secretary to determine whether parcels of surplus federal property were suitable for use as local airports and to recommend that such parcels be transferred to local authorities if the transfer would not interfere with the agency's needs.

The GSA, however, has steadfastly ignored the handful of recommendations it has received, contending that the Surplus Property Act of 1944 requires it to screen surplus properties for potential local use, but does not require that the property be transferred.

Earl Jones, commissioner of the GSA's Federal Property Resources Service, said the Reagan administration is still committed to selling surplus property rather than giving it away.

As a result, Sen. Daniel K. Inouye (D-Hawaii) has introduced legislation that would strip the GSA of its authority over potential airport properties. Jones vowed that the administration would fight the effort.