Office of Management and Budget officials, hunting for new cuts in the federal budget, want the Agriculture Department to stop giving the school lunch program free supplies of surplus butter, cheese and milk and make the program--and ultimately children's families--pay for the dairy products instead, according to sources in both agencies.

The idea, which could mean a budget savings of $300 million, is meeting strong resistance at USDA, where the giveaway program solves two problems simultaneously. Last year, the policy allowed USDA to get rid of about 25 percent of the butter and 20 percent of the cheese it bought under the dairy price support program. It also meant USDA was able to provide the school lunch program with 50 percent more meat, bread, fruit, vegetables and dairy products than it would have been able to contribute otherwise.

Right now USDA is trying to figure out how to give away 225 million pounds of surplus cheese before it spoils and the school lunch program is one possible recipient, along with other feeding programs.

According to officials at both agencies, the long-running debate over the dairy giveaway is likely to resurface during deliberations over the fiscal 1983 budget.

USDA's Food and Nutrition Service, the agency that administers the school lunch program, announced in yesterday's Federal Register that it has followed Congress' instructions and cut back contributions of food to school lunches from about 14.5 cents' worth a meal last year to 11 cents a meal this school year.

These in-kind contributions of meat, poultry, grains, fruits and vegetables will total about $407 million this year, according to USDA's Marvin Eskin--down from about $615 million last year. The donated food makes up between 15 and 20 percent of the school lunch program's total budget, which has dropped to $2.3 billion in fiscal 1982 from $3 billion last year.

The meat, poultry, fruits and vegetables involved are regularly purchased by USDA to stabilize their markets--an informal price support effort. The Food and Nutrition Service uses some of its budget authority to "buy" some of these products from other USDA agencies, then sends them out to the schools.

But last year, in addition to spending $615 million on these products, the service sent schools $311 million worth of surplus dairy products free--including 90 million pounds of butter and 106.5 million pounds of cheese.

This bonus program, which has existed in some form since 1978, is what some OMB officials want to abolish. Instead, it wants the Food and Nutrition Service to pay for the milk, cheese and butter the same way it pays for its chicken and peas.

The change would eventually mean higher prices for many of the 26 million children in the program, according to Joanne Styer, who directs food programs for the Montgomery County public schools.

The most recent sign of OMB's continuing effort to end the bonus program came when the Food and Nutrition Service sent its Federal Register notice to OMB for clearance--as required under President Reagan's executive order on regulations. OMB made one major change: it deleted a sentence saying the existing bonus program would continue. The deletion does not mean USDA's policy will change, only that the change will be easier to make in the future.