The White House has nearly completed work on a list of additional cuts and changes in the current 1981 federal budget that are intended to demonstrate new savings of perhaps $4 billion, according to sources in the administration and on Capitol Hill.

These new reductions, many of them based on bookkeeping technicalities, may be announced this week or next, according to administration officials. They are designed to prove to a skeptical Wall Street financial community the Reagan administration's determination to hold down spending.

Some of the new cuts will require votes of Congress to formally rescind or defer appropriations already made. Some of the affected programs are job training, student loans, environmental protection and the national endowments for the arts and humanities.

The new reductions are needed if the administration is to meet its own optimistic goals for controlling government outlays and the federal deficit in 1981. Because interest rates have risen much higher than the new administration had predicted, it is now certain that government outlays will be considerably higher than the president forecast earlier this year. The government pays market interest rates on the money it borrows to finance the federal debt; higher interest thus means higher outlays.

The White House has known for some weeks it would have to find additional ways to reduce 1981 spending, but efforts to make those reductions became intense in the past fortnight, according to a senior official.

A spokesman for the Office of Management and Budget said the administration is now hoping to hold federal outlays to $660 billion, $5 billion more than originally planned. Instead of a $55 billion deficit, the White House now hopes to keep the final figure under $60 billion.

The government's inability to meet optimistic targets is one source of the Wall Street anxieties that have sent interest rates soaring in the last few weeks.

However, the White House has also found that congressional tolerance for budget-cutting is not limitless. The Senate proved the point last week when it voted 96 to 0 against the president's last cost-cutting plan, a major revision of the Social Security program. Such votes also contribute to jitters in the financial markets, where they are interpreted as a sign that Congress eventually will gut the Reagan economic program.

This leaves the Reagan administration caught between a desire to continue its winning ways in Congress and a desire to continue cutting domestic spending to limit the budget deficit.Some Republican leaders on Capitol Hill reportedly have warned the White House that Congress can't tolerate another wrenching round of budget cuts now.

The White House is known to be fearful that an announcement of further budget cuts could complicate its efforts to win final congressional approval for rescissions from the 1981 budget. Both houses have approved versions of those cuts, and a conference committee is scheduled to start working out a final version the first week of June.

Rumors of new cuts in agency budgets swept through Washington at the end of last week, and several agencies were advised formally that they could expect to be the targets of new cuts.

One was the National Endowment for the Arts. The White House and OMB informed the endowment that it was one of about 125 agencies or programs that would be cut back in the next round of reductions. The agency previously had been targeted for big cuts in 1982, but not this year.

If the White House plan is approved in Congress, according to sources in the agency, the arts endowment's 1981 outlays will be cut by $13 million and its ability to obligate future spending by $32 million. There will be similar cuts at the National Endowment for the Humanities.

The Department of Education learned that OMB planned modest cuts of about $15 million by making technical changes in the National Defense Student Loan Program and the Law Enforcement Education Program, both of which provide loans to college students.

At the Labor Department rumors were rife of further cuts in job-training programs, already a principal target of the new administration. Staffers at the Environmental Protection Agency said they expected to lose $120 million from their 1981 budget.

Bigger "savings" may be made by reestimating the rate at which the government will spend money between now and the end of the fiscal year (Sept. 30) on a few big programs, particularly defense and unemployment compensation. Outlays on both of these have been slower than anticipated this year, so budget money probably won't all be spent by Sept. 30, according to government officials.

The administration also will be able to report a "saving" of about $500 million by dropping its plan for a July pay increase for military personnel. Congress has already demonstrated its distaste for this proposal, so the White House can now drop it and take the budgetary benefit, an OMB official said.

White House officials say there are other administrative methods that can be used to control the outflow of government funds for this fiscal year. Budget director David A. Stockman has been discussing these bookkeeping devices with Cabinet officials, according to a senior White House aide.