Only one-fourth of $40.7 billion that President Reagan's team at the Pentagon says will be saved over seven years through better management can be verified, the General Accounting Office said in an internal report obtained yesterday by The Washington Post.

This finding by the congressional agency after its most extensive review of the claimed savings is likely to turn up the heat in the debate over whether Reagan is getting enough bang for the buck as he tries to rearm the nation.

The GAO stated in its draft report that it reviewed $40.7 billion of the $52.4 billion that Defense Secretary Caspar W. Weinberger last year estimated would be saved from 1981 through 1987 through management changes he and his colleagues have instituted at the Pentagon.

After studying Pentagon documents and interviewing military officials in Washington and in field commands, the GAO said it could verify only $10.7 billion in savings.

The agency characterized more than $25 billion of the $40.7 billion it reviewed as "questionable" and $4.4 billion as "not supported."

A Pentagon spokesman said the GAO "misinterprets the object of what the Defense Department was trying to do in listing for Congress money to be saved through a number of reforms. The idea was not to take credit for savings but to show how much additional money would have to be spent, or programs canceled, if it were not for the economies made by both the Congress, the Defense Department and the administration. Also, the GAO in its draft report credits us with savings we did not claim but fails to compute them in arriving at its totals."

The Senate Armed Services Committee last year asked the agency to review the $52.4 billion in savings claimed by the Pentagon.

"We do not believe that the claimed savings from the proposed economies and efficiencies were adequately supported," the GAO stated.

"We believe collectively these actions will reduce spending," GAO said, even though its auditors concluded that the administration cannot take credit fairly for the advertised $52.4 billion total in savings. In sifting through the savings claimed by Weinberger, the GAO included these in its "questionable" column:

* $19.2 billion from the civilian pay freeze that Congress legislated.

* $4.3 billion from reforming military retirement benefits under a Carter administration plan that the Reagan administration has rejected.

* $2.3 billion in reduced travel and consulting services because the Pentagon took the savings from one or two years and assumed without further guidance and documentation that they would be repeated in subsequent years.

"Air Force officials told us," the GAO report said in citing one example, "that the fiscal 1983 reduction was a one-time reduction and they had received no guidance on any further reductions in administrative travel."

Only after the Pentagon sent Congress on Feb. 8, 1982, a list of "economies and efficiencies" did the Defense Department controller tell the military services and others how the savings were to be identified and computed, the GAO said.