Federal grants to District programs would be cut by $44.4 million under President Reagan's proposed fiscal 1987 budget, according to a study by the D.C. City Council budget director.

The study, which noted that some programs would receive funding increases, cautioned that "the numbers are bound to change as Congress and the White House reach compromise" in the coming debate over the federal budget.

Cuts in federal grants would be particularly damaging to programs administered by the D.C. public schools and the departments of Employment Services, Human Services, and Housing and Community Development, according to the study by Budget Director Rich Siegel.

The analysis is expected to provide guidance to the City Council in its upcoming hearings on a $2.4 billion budget proposal submitted Jan. 31 by Mayor Marion Barry.

The study also noted that while the Reagan budget proposed a $19.5 million increase in the annual federal payment to the city, other costs imposed on the District by the president's proposal would more than offset the increase.

Referring to the automatic cuts mandated by the Gramm-Rudman-Hollings law if the federal budget does not achieve the required deficit reduction target of $144 billion, the study stated that, "Whether Gramm-Rudman-Hollings or the president's budget proposal or a combination of the two is adopted by the Congress and the president, it's going to be bad for the District."

Siegel concluded that the adverse effects would be greater if the Gramm-Rudman-Hollings cuts are triggered for fiscal 1987.

A federal court panel ruled last week that the trigger provision is unconstitutional. The matter is likely to be resolved on appeal to the Supreme Court.

Other highlights of the effects of the president's proposed budget on the District:

*Elimination of a $5.7 million Community Services block grant that would have a "major impact on the overall delivery of social and family services."

*The loss of more than $13 million to higher education institutions because of the "virtual elimination" of Pell Higher Education grants and the "entire elimination" of Supplemental Education Opportunity grants and the College Work Study program.

*Increases in the budget that could offset some of the cuts. The analysis reports that while $44.4 million in program grant cuts have been proposed based on a 1986 level of $520.1 million in federal grants to the District, increases in other program areas within the District total $7.1 million.