As a rule, advice from an outgoing administration to an incoming administration of the opposite party is as welcome and useful as a Doberman in a dinghy. Especially is that true when the topic is the structure of the White House staff and the advice is coming from one president's aide to those serving a very different individual.

Notwithstanding all those cautions, there is one message the departing Jimmy Carter aides have been trying to wigwag to the incoming Ronald Reagan officials that may be worth their considering. It is a plea to continue the Carer innovation that links Cabintet coordination and intergovernmental relations in a single White House office.

That sounds dry as dust, but it can have powerful governmental and political implications. Where an officed is in the White House hierachy determines its leverage and the degree of influence its constituents enjoy. Carter's decision elevated the access and influence of governors and mayors, and Reagan's battle plan drops them back to a pre-1976 stance.

As outlined last weekend, the Reagan White House plan separates intergovernmental relations from the Cabinet secretariat about as far as possible in the same building. Intergovernmental relations is one of seven staff functions reporting to chief of staff James A. Baker III. The person handling the job of dealing with state and local officials (so far unnamed) will have the same status -- no more or less -- as the person dealing with the interest groups, out-of-town editors and broadcasters, and the White House press corps. Cabinet coordination will be done separately by a staff responsible to Baker's opposite number, counselor to the president Edwin Meese III.

Reagan officials with whom I discussed this question said they thought Carter had made intergovernmental relations an additional responsibility for the secretary of the Cabinet in order to give his own transition chief, Jack . Watson Jr., a bit more to do than shuffle papers from the departments to the Oval Office. But Watson tells a very different story of the origins of the decision.

He says Carter, like Reagan, was a former governor who was often frustrated in his efforts to pull together at the state level programs that were based in several different Cabinet agencies. By linking intergovernmental relations and Cabinet coordination at the senior White House staff level, he intended, Watson says, to do two things.

One was to give governors and local oficials a single spot where they could get answers to their questions in Washington. The second was to give their man in the White House enough clout with the Cabinet that the departments and agencies would have to consider the views of state and local officials.

Unlike a lot of other things Jimmy Carter attempted, this one seems to have worked. Watson was in the dual job for three years before succeeding Hamilton Jordan as chief of staff. He and his deputy and successor, Eugene Eidenberg, and Eidenberg's deputy, former Iowa legislator Tom Higgins, built a unique set of personal and political networks across the federal government and into state capitols, county courthouse and city halls.

"By linking the intergovernmental relations office to the Cabinet secretariat," Eidenberg says, "we gave the local and state officials more access to decision-making than they had ever had before." Higgins adds that the other side of that coin was that "state and local officials felt for the first time they were as important a political constituency for the White House as Congress was."

Proof of the political utility of the arrangement was the way that governors and mayors rallied to Carter's support, in the face of Ted Kennedy's challenge to his renomination, when most Democratic members of Congress gave Carter lip service or the back of their hands.

Although they are partisan Democrats, Watson, Eidenberg and Higgins all share Reagan's belief that the web of federal regulations has become an oppressive burden -- impeding the ability of state and local elected officials to target government resources effectively on the needs of their own constituencies.

"In our second term," Eidenberg says, "we hoped to bring Congress along to see its interest lies in giving more flexibility to the states and localities -- to hold them accountable for the delivery of services but to let them figure out the best way to deliver them."

The political turnover in Congress makes that goal more attainable by Reagan than it would have been by Carter. But to do it well, his White House and administration will have to be sensitively attuned to what the state and local officials are saying.

"That's quite a talent pool out there," Eidenberg says. "Whatever their structure here [at the White House], I hope they bring them in even more than we did, and test the Washington attitudes against the wisdom of the people who are running states and cities and who are ultimately accountable for delivering the services people want. I hope they bring them in."