Ambassador William E. Brock, the United States Trade Representative nominated by President Reagan to be secretary of Labor, has urged the White House to name his successor as promptly as possible to help bolster morale at the trade office, and to assure America's partners abroad that the U.S. still gives trade issues a top priority.

Officials said last night that no candidate had emerged as a clear favorite, but that they hoped a new trade representative would be chosen by next week.

Staffers at the trade representative's office fear that a delay in appointing a new trade ambassador might create a vacuum, and lead to a revival of Commerce Secretary Malcolm Baldrige's proposal to combine the Brock office and Commerce into a new Department of Trade and Industry. This idea was shelved by the president -- at least temporarily -- this past week.

But a Commerce Department spokesman said Baldrige acknowledges that the trade issues are too pressing to allow the trade post to remain vacant. Baldrige recommended Under Secretary of Commerce Lionel Olmer for the job, but it was reported yesterday that the White House has ruled Olmer out.

Other prospective candidates on an initial White House short list who have declined the job include former New York congressman Barber Conable, and Ed Pratt, chairman of Pfizer Inc., and a member of the Emergency Committee on American Trade. Conable, who was sounded out by the White House, told The Washington Post that he might return to government at some point, "but not for a year or two."

Walter B. Wriston, retired chairman of Citicorp, who originally was recommended by White House Chief of Staff Donald T. Regan, is being considered, but no longer heads the list of candidates, sources said.

A more likely candidate, one informant said, is Rep. Bill Frenzel (R. Minn.), ranking Republican on the House Ways and Means trade subcommittee. Frenzel, 56, is highly regarded as an authority on trade matters on both sides of the aisle in the House. Conable suggested that Frenzel would be the best possible successor to Brock, but said Frenzel "will leave a gaping hole on the committee, where he's desperately needed."

Other prospects said to be under consideration by the White House include William R. Pearce, of the Cargill Co., who was deputy special trade representative in the Nixon administration; Edson W. Spencer of Honeywell Inc., who has wide experience in U.S.-Japanese relations; Donald Rumsfeld, former secretary of Defense and now chief executive officer of G. D. Searle & Co.; and Clayton Yeutter, president of the Chicago Mercantile Exchange, a former deputy trade representative and a former assistant secretary of Agriculture.

Talent scouts at the White House are seeking a prospect who not only knows trade issues, but a person who can deal with Congress. "Whoever Reagan picks," said a Capitol Hill source, "he'll find that he spends as much time negotiating with committees up here as he does with other governments."

Although Brock said at the White House Wednesday when the president announced his appointment that he is looking forward to a new challenge at the Labor Department, it was learned that he agreed to the move with some reluctance, given the delicate nature of current trade negotiations with Japan, and the preliminaries to a forthcoming new round of multilateral trade negotiations.

Regan was the originator of the idea to move Brock to Labor, and applied heavy pressure. Others in the administration -- including Secretary of State George Shultz -- were reluctant to see Brock leave the trade post. President Reagan was the final persuader.