In the search for ways to narrow the $200 billion deficits expected the next few years, the White House has been turning over almost any stone that looks as if it could yield new savings and doesn't have "Social Security" written on it.

President Reagan's budget "core group" has been devoting lots of attention to ideas left over from the first term, such as slashing mass-transit subsidies and urban development action grants.

But every budget cycle also gives birth to a few fresh ideas -- the kind that never make it into the budget. Two examples from this year:

* Abolish the Council of Economic Advisers. Aides figured the savings would be minimal, but the symbolism might be powerful, coming from a president who declares his disdain for economic projections and has left the chairmanship of the council vacant since Martin S. Feldstein departed last summer.

* Sell off to the private sector the federal government's financial assets, such as student loans or Farmers Home Administration loans that are owed to the government. "We probably could get 20 cents on the dollar," said one bemused budget official.

Both ideas reportedly have been scrapped for this budget cycle.

BETTER LUCK NEXT TIME . . .

Reagan's Cabinet members may have more trouble appealing budget cuts to the president than in the past. This time the process has been "front-loaded," with Reagan personally going over the budget, item by item, in search of savings.

In the past, Office of Management and Budget Director David A. Stockman came up with cuts, Reagan approved them, and the Cabinet members came back with specific appeals. This time, Cabinet members may appeal, but the decisions they attempt to overturn will have been made in the first instance by Reagan, not Stockman.

"I don't know what the president is going to tell them" when the Cabinet meets this week, says a White House official. "Maybe he'll say, 'You can appeal, but good luck.' "

INTO THE DEEP FREEZE . . .

Since the election, White House counselor Edwin Meese III has been very active in domestic policy, insiders say.

Many of the ideas generated by Meese's subordinates have been shunted aside in the more urgent budget deliberations, but officials say Meese was responsible, at least in part, for Reagan's embrace last week of a so-called freeze in federal spending.

Over the Thanksgiving holiday, Stockman had put together a plan that envisioned deep cuts and selective elimination of many domestic spending programs. This was the "Draconian" plan -- designed to reduce the deficit without tax increases or cuts in Social Security and defense.

But some Reagan aides balked at the depth of some of the cuts in Stockman's plan. Meese then suggested that Reagan try to meld it with a spending "freeze" that would keep next year's budget at this year's levels.

The result is a blending of both Stockman's "black book" of cuts and Meese's idea of a "freeze." In every program, Reagan is being asked to choose among three options: freeze at current levels, reduce or eliminate. Of course, Reagan must go well beyond a "freeze" to reach his goal of $42 billion in cuts next year. Reagan aides say a freeze would net only $17 billion of the needed cuts.

White House aides like the freeze concept because it rings true on Capitol Hill and implies maintenance of the status quo instead of painful new cuts in popular programs. But it is not a new idea. Stockman wrote in last year's budget that Reagan had put into place "a decade-long domestic real spending freeze."

That meant that domestic spending (everything but defense, net interest and programs such as spending on space and foreign aid) was not rising faster than inflation. This year, more stringent goals would aim at holding the overall budget at last year's level, regardless of inflation. With Social Security and defense growing, the only way to do that is to cut many programs sharply and throw others "overboard," as some aides put it.

END RUN FOR RUCKELSHAUS . . .

William D. Ruckelshaus experienced his share of frustration with White House aides in the 18 months he just completed as head of the Environmental Protection Agency. One big frustration was his inability to win Reagan's approval to mount a major offensive against acid rain.

But Ruckelshaus bypassed some White House lieutenants in the end with an unusual back-door move.

Ruckelshaus went to Reagan to submit his resignation and, at the same time, obtained the president's commitment, on the spot, to name Lee M. Thomas as his successor. Most of the White House staff became aware of the maneuver only after the decision was made.