The Reagan administration has begun sounding out key congressional leaders privately on the possibility of a compromise on the president's controversial tax-cut proposal.

The message cane in exploratory talks yesterday and Wednesday between Treasury Secretary Donald T. Regan and leaders of the House and Senate tax-writing committees.

Although no specific concessions were discussed, sources said the Treasury secretary hinted that the administration might agree to less than a full three-year cut if the rest of Reagan's plan were approved relatively intact. The president has proposed a three-year, 30 percent tax cut.

Regan reportedly also appealed to the tax-writing chairmen to urge their members to set aside their own favorite proposals for other tax incentives for the administration's second tax bill, to be sent to Capitol Hill later this year.

Sources described the talks as only preliminary, and stressed that neither side made any specific compromises. However, the meetings were a definite signal that the administration is beginning to ease its no-compromise stand.

The developments came as evidence continued to mount that the president's three-year tax-cut plan is meeting resistance in Congress. Yesterday House Minority Leader Bob Michel (R-Ill.) conceded there weren't enough votes in the House to pass the Reagan bill intact.

Meanwhile, the administration continued to insist publicly it had not changed its position on any compromise. White House spokesmen quoted President Reagan as saying, "I have not changed my opinion one bit."

Reagan's meeting yesterday was with House Ways and Means Committee chairman Dan Rostenkowski (D-Ill.). On Wednesday, the Treasury secretary met with Sen. Bob Dole (R-Kan.), chairman of the Senate Finance Committee.

Regan later left on a nine-day trip to Suadi Arabia and other Middle East countries. Insiders speculated it was unlikely there would be further action on the tax bill until he returns.

The approach to congressional leaders came as top White House officials held a round of high-level meetings over the past few days to discuss the tax-bill issue, apparently without agreeing on a definite strategy.

While the White House was deliberating its next move on the tax plan, economist Alan Greenspan, a Reagan adviser during the 1980 campaign, told the Senate Finance Committee yesterday that the tax plan's prospects have "recorded in recent months."

The outlook for the tax-cut plan has been clouded by three factors: Soaring interest rates are pushing the budget deficit out of hand, the bond market is in a tizzy over the rise, and Congress is becoming wary of the tax-cut bill.

"There's been a lot of thinking going on," one administration official said yesterday. "But so far, nothing's come of it. The questions have been raised, not answered."

What administration officials would like to do is try to cope with all three problems by reducing the fiscal 1981 budget deficit. A new round of spending cuts drafted by Office of Management and Budget Director David A. Stockman may be unveiled soon.

An unofficial tally of the Senate Finance Committee shows only six of the committee's 20 members fully support the president's tax-cut plan intact. The rest want to replace major parts of Reagan's plan with their own proposals.

In the House Ways and Means Committee, Democrats are solidly against enacting Reagan's three-year plan intact, but haven't been able to agree on any single alternative. Further caucuses are expected next week.

There still is no fallback position in case the administration does have to bargain. But insiders say the talk probably would center on postponing the first year of the tax reduction, not watering down its size.

Reagan's current proposal calls for tax reductions of 10 percent a year for each year of the next three years, combined with faster depreciation writeoffs for business and a series of minor proposals.

One compromise might be to delay the first year's reduction in 1982, and begin the tax-cut program intact right then. Or the first-year cut could be trimmed to 5 percent, with the remainder postponed until a fourth year.

At a meeting of the Finance Committee yesterday, Dole tried to smooth over differences on the Reagan plan, contending that members aren't "that far apart" and "could reach agreement very quickly.

However, strategists point out that the Democratic-dominated House gets first crack at any tax bill -- and the administration's best shot at compromise won't come until the measure goes to the Senate.