President Reagan will send Congress a $973.7 billion budget request for the next fiscal year that proposes major cuts in many domestic programs but falls short of the president's goal of cutting the deficit in half over three years, White House officials said yesterday.

Although the White House had hoped to reduce the more than $200 billion yearly federal deficit to $100 billion by 1988, the spending blueprint that Reagan will send to Congress Monday, if fully enacted, would reduce the deficit to $144 billion in that year.

The deficit projected by the administration for next year would be $180 billion. Reagan came into office in 1981 promising to balance the budget by 1984.

Congress, however, is unlikely to accept the proposed fiscal 1986 budget as is. Some of its spending cuts are controversial and Democratic and Republican lawmakers have indicated they would like to scale back its proposed $314 billion in defense budget authority.

Senate Republicans have been trying to fashion their own version, based on an across-the-board budget freeze.

Reagan's proposed budget is 1.5 percent above this year's estimated $959 billion, one of the smallest rates of increase in years. It would not allow government to keep pace with inflation, estimated to run at about 4.3 percent next year.

The budget proposal would freeze total spending on government programs at current levels, with defense allowed to rise by $29.2 billion and many domestic programs taking offsetting cuts of $39 billion, administration officials have said. Interest on the national debt also would continue to rise.

Although the budget has been embargoed for submission to Congress on Monday, its details have been filtering out for weeks -- as with nearly every budget over the last few years. The final figures are almost identical to those presented weeks ago by Office of Management and Budget Director David A. Stockman to members of Congress.

Interest groups, from environmentalists to veterans, have known the details of cuts in their areas for weeks and have been gearing up to fight to protect their programs.

The budget proposal seeks to trim $50 billion from the deficit next year, the figure that Federal Reserve Board Chairman Paul A. Volcker has told Congress is the minimum necessary to induce a decline in interest rates.

The package of budget cuts is roughly equivalent to what Reagan proposed when he first took office in 1981. However, Reagan this time has targeted many politically sensitive, largely middle-class programs that Congress has refused in the past to trim. In 1981, the programs cut most severely were those affecting the poor.

According to documents given to lawmakers this week by Stockman, the budget next year will reduce funds for college student aid by about $700 million, for veteran programs by about $1 billion, for farm price support programs by about $2 billion, for the Small Business Administration by about $1.5 billion and for urban mass transit by about $800 million.

In addition, the budget proposes a variety of changes in Medicare and Medicaid to save about $5.2 billion, and a one-year delay on cost-of-living adjustments for social entitlement programs, except Social Security. That would save $2.6 billion. Federal workers would be asked to take a 5 percent pay cut, for a savings of $1.6 billion. Reagan's budget proposes no major tax increases.

White House spokesman Larry Speakes said yesterday that Reagan's strategy is to reach agreement quickly with Senate Republicans on a compromise budget.

The Republicans, led by Senate Majority Leader Robert J. Dole (R-Kan.) had expected to unveil their budget proposal by yesterday but were unable to meet the deadline.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said this week that the GOP senators agreed on two-thirds of that proposal but could not agree on several areas, including defense.

A Senate GOP official said yesterday that it now appears the Republicans will not offer their proposal until after the February congressional recess, which ends Feb. 18.

Dole and Domenici, along with other key lawmakers, were to receive their copies of the budget request this morning and were planning to meet with Stockman today to discuss it.

Administration officials have acknowledged that in any compromise the Republican senators would have to include a smaller increase in defense spending than Reagan is seeking.

Some senators are pushing for a freeze on defense spending, which would knock $20 billion off the deficit, but Reagan has said there is no more room for defense budget savings.