The Reagan administration's proposed budget cuts may cost more than 30,000 jobs in the Washington region, according to a report prepared for the area's governments.

The report, a preliminary analysis of the impact of the budget cuts on the Washington metropolitan area prepared by the Council of Governments, said that the cuts would take a toll in three major areas -- loss of federal employment and the additional jobs in the private sector produced by those federal workers spending their pay, loss of federal grants to local and state governments and loss of federal contracting dollars.

On the positive side the report notes that the area's economy has become increasingly diversified in the past decade. "Continued high growth in the private sector in the 1980s will be the pivotal factor in the region's ability to absorb laid off federal workers," according to the report.

"The loss of income to the regional economy through reductions in federal employment could be much more significant than reductions in federal grants to local and state governments," the report said. Because federal employment is a more significant part of this area's economy than it is in other areas, cutting back the number of federal workers hits the Washington area particularly hard.

The report predicts a loss of 16,000 federal jobs in the Washington area by fiscal 1982. Those workers normally would be expected to spend almost $300 million in the regional economy, the COG report said. It also estimated that each federal job generates another job in the private economy.

In terms of direct assistance to local governments, the analysis predicted that the most significant program reductions in the Washington area would be reduced spending for primary and secondary education and transit operating assistance.

"During fiscal year 1982, it has been estimated that local governments will receive $43 million less in impact aid, categorical grants, vocational education and school lunch programs," the COG report said. It added that the proposal to eliminate all operating subsidies to transit systems would delete $28 million from the Washington Metropolitan Area Transit Authority's income.

The region also will be affected by cuts to programs that provide assistance to low-income individuals and families through local or state agencies, such as welfare and subsidized housing.