The State Department is preparing to train and dispatch across the nation a special team that will seek to sell the embattled policy of "constructive engagement" with South Africa.

The dimensions of the salesmanship effort for the controversial policy are yet to be determined, department officials said. But several familiar with the discussions compared it with the Carter administration's public relations programs to back ratification of the Panama Canal treaty, the SALT II strategic arms control treaty and the Reagan administration's effort to promote its Central American policies.

The Senate is likely to vote final passage of a bill requiring economic sanctions against South Africa in the second week of September, despite strong objections from the White House and the State Department. President Reagan is reported to be prepared to veto the measure and to adopt some of its provisions by executive action.

Senior administration officials continue to say, in public and private, that they see no viable alternative to a continuation of the "constructive engagement" policy aimed at working cooperatively with South Africa's white regime.

Frank G. Wisner, deputy assistant secretary for African affairs, said a special public affairs effort is being considered because "we've been swamped with requests" for speakers on the subject.

"We need to have a few more than the tiny band of two or three people" to make the case, Wisner said. He added that "we haven't come to any conclusions about the public relations program and won't do so for another week or so."

Robert M. Smalley, deputy assistant secretary for public affairs, said, "We are going to explain what U.S. policy is, defend it, express it, explain it. There is an enormous demand for information out there."

Smalley said, "There is precedent for taking a headline issue and getting the information out," but added there is no agreement yet on the dimensions of the "contructive engagement" effort.

John T. Sprott, acting director of the Foreign Service Institute, said no request for large-scale training of State Department officers in presenting the South Africa policy has been received by his organization. He said FSI has worked on a program to provide three days of public speaking and South Africa policy training to a number of officers, "less than 20," before the end of this month.