President Reagan has given tentative approval to a package of $34 billion in domestic spending cuts for next year and intends to deliver a firm message to his Cabinet today that he does not want to overturn the cuts on appeal, administration officials said yesterday.

The $34 billion falls short of the White House goal of $42 billion in savings for next year. The $8 billion difference may be made up with a slowdown in defense spending, officials said. It was also learned that Reagan's lengthy review of the budget had not yet identified enough savings to reach the goal of slashing the deficit in half by 1988, from more than $200 billion.

Sources said the administration's "core group" of fiscal experts was less than 80 percent toward that goal for 1988.

Office of Management and Budget Director David A. Stockman spent yesterday discussing defense spending issues with Reagan and his advisers. Stockman has a detailed plan for reducing defense spending by $8 billion next year, $20 billion in 1987 and $30 billion in 1988. But aides said Reagan wouldn't reach a decision until Defense Secretary Caspar W. Weinberger returns from overseas next week.

Also yesterday, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said that from his "personal standpoint" Social Security cost-of-living adjustments (COLAs) should not be "off limits" to budget cuts if included in a package.

At a breakfast meeting with reporters, Domenici said, "I won't be reluctant to propose something" in the way of restraint in all federal cost-of-living adjustments. "It may very well turn out that a basic freeze or something like it will be preferable to what's being worked on" by the White House, he said. "If that's the case, a Social Security freeze will be in there."

Reagan has said that Social Security is off limits for tampering or budget cutting. But Domenici and other Republicans have been talking about an across-the-board budget freeze that might include both Social Security and defense spending. The White House is considering a freeze on total spending, but with deep cuts in programs offset by increases in Social Security and defense.

Domenici emphasized that he would attempt to bring the deficit down without cutting Social Security COLAs, but said, "I have no doubt" that Congress would consider cuts in all the annual cost-of-living adjustments.

He also said the planned defense budget increase could be slowed down "significantly."

If Reagan wins every dollar from Congress in the proposed $34 billion package, which is not likely, it would be close to the $36 billion in cuts he won in the most successful budget-cutting year of his first term, 1981. As expected, the package includes cuts in federal health, agriculture, veterans' and retirement programs, as well as reductions and some outright eliminations in other nondefense spending.

An administration official said Reagan probably would not accede to Cabinet members' appeals of cuts, unless they find offsetting ones in their own departments. The official noted that Reagan was more involved in deciding where to cut this year than in the past and thus would be less inclined to reverse decisions already made.

Also, officials said Reagan probably would not propose an ambitious $7 billion expansion of foreign aid discussed by top national security officials because of the deficit.