President Reagan will ask Congress to cut federal arts and humanities spending by just over $35 million in the fiscal 1987 budget plan he will send to Capitol Hill early next month, knowledgeable sources confirmed yesterday.

It will be the fifth year in a row that the Reagan administration has sought substantial cuts in the budgets of the National Endowment for the Arts and the National Endowment for the Humanities. Last year the administration proposed a similar reduction of more than $30 million, but congressional opposition led to a compromise plan that held arts spending steady in fiscal 1986.

This time around, there will be increased pressure on arts boosters because of the Gramm-Rudman-Hollings budget-balancing law passed by Congress late last year. Gramm-Rudman requires that the federal budget deficit be reduced to $144 billion in fiscal 1987.

"It's going to be a lot tougher to win this time," said Robert Lynch, executive director of the National Assembly of Local Arts Agencies, whose members depend heavily on NEA grants. "We'll have to work harder just to stay the same."

Sources said President Reagan's 1987 budget will seek to cut NEA's budget from $165.7 million to $145 million, or 12.5 percent. The administration will ask for a 10.4 percent cut in the humanities budget, from $140.6 million to $126 million, the sources said.

The National Endowment for the Arts refused to comment on the specific cuts the administration reportedly will propose, but it released a statement yesterday that expressed general support for Reagan's budget-cutting efforts. "The National Endowment for the Arts understands the need for Gramm-Rudman across-the-board cuts," the statement said. "Implementation of these cuts will not significantly hurt the endowment's ability to support the arts."

But Lynch said that even a relatively small cut in NEA's budget will have a major "trickle-down effect" on local theaters, symphonies and galleries across the country. In the event of a cut, he said, "the states or local governments or corporations will say, 'If the federal government is not supporting this at the level it was, then why should we?' That's something we see over and over again."

"Already we're seeing people not doing the risk-taking things they've done before," said Anne Murphy, executive director of the American Arts Alliance. Murphy said that because the federal arts budget has been in a "hold-even position" since 1981, "you're seeing more emphasis on the commercial side of nonprofit art. I don't think that bodes well for the future."

Congressional allies of arts groups such as Lynch's and Murphy's reacted cautiously yesterday to the reports of a renewed attempt to slash federal arts spending. Rep. Sidney Yates (D-Ill.), chairman of a House subcommittee that oversees the NEA and NEH budgets, told reporters that it was too early to comment on Reagan's proposals for fiscal 1987. Yates said that he would wait until all of the administration's proposed budget cuts were available for analysis before voicing his reaction.

Sen. Claiborne Pell (D-R.I.), another congressional arts supporter, also said he "would like to see the arts portion in the context of the president's entire budget." Pell added, however, that he understood "that arts funding is not exempt from budget pressures."

Office of Management and Budget spokesman Edwin Dale said that he would neither confirm nor deny the reports of President Reagan's proposed arts cuts. But he said the president would seek to reach Gramm-Rudman's $144 billion deficit ceiling by proposing $50 billion in cuts of "nondefense" federal programs.