The Reagan administration, under growing congressional pressure over trade, is considering a major policy shift to support a program that would impose a fee of up to 1 percent on imports in order to provide an estimated $250 million in job-training aid to workers who lose jobs because of foreign competition.

Senate and House committees have approved measures that would extend -- and significantly expand -- the Trade Adjustment Assistance program beyond its current expiration date of next Monday. President Reagan had previously called for scrapping trade-adjustment aid because of its cost and because of criticism that it failed to provide useful retraining.

The Senate Finance Committee last week unanimously approved a bipartisan bill that would fund retraining by imposing an import "user fee" ranging from one-tenth of one percent to one percent of the total value of U.S. imports. The revenue would be used to pay up to 52 weeks of additional unemployment benefits to an estimated 30,000 workers per year, provided they are enrolled in an accredited retraining program.

The bill, sponsored by Sens. William V. Roth Jr. (R-Del) and Daniel Patrick Moynihan (D-N.Y.) and others, would give dislocated workers in the program a $4,000 "retraining voucher" to go toward finding work in a new industry.

At the White House, the administration's economic policy council yesterday discussed reversing the administration's position and backing the Senate bill or writing its own version, according to administration sources. But the sources said strong objections remain to parts of the Senate bill, and Cabinet members deferred action pending more study.

Administration sources said Cabinet members were considering urging the White House to back some type of assistance program as a means of showing the president's concern about the impact of foreign imports and also heading off potentially more costly and protectionist trade-related bills.

Senate sources, meanwhile, said the current program would likely extend beyond Sept. 30 under the continuing resolution approved by Congress for the federal budget.

Trade Adjustment Assistance, created in 1962, ballooned into a massive unemployment program in the late 1970s when the flood of steel and auto imports helped throw hundreds of thousands of workers out of jobs. More than 500,000 workers qualified and spending ballooned to about $2.7 billion in 1979.

The Reagan administration has already cut back on the program, tightening eligiblity and requiring recipients to first exhaust all other unemployment benefits. Spending for the program is about $115 million a year.

The Roth-Moynihan bill, applied to the current level of $350 billion a year in foreign imports, could create a trust fund of up to $3.5 billion annually through the user fee. But the president would have power to set the fee, and Senate sources said the program could operate on about $250 million a year.

Labor Secretary William E. Brock, at Reagan's direction, heads a Cabinet working group to consider "adjustment" for dislocated workers. Brock supports some form of trade-adjustment aid, but has not given his position on the current bills. The House Ways and Means Committee has approved an extension of the current program in a simpler version than the Senate bill.

"I am very much encouraged by the administration's review," Roth said in an interview, "I think you will see a changed position . . . I think we have largely answered [the criticisms] by the user fee. After all, those who profit from trade should help pay the cost."

Roth also said that his bill deals with the other major criticisms that the previous program allowed dislocated workers to collect benefits even after they got jobs or had given up looking for work. The current bill would prohibit that by linking it directly to job training.

Regarding the Roth-Moynihan bill, a White House official said it appeared that "we're going to get stuck with it" because it is attached to a budget reconciliation bill that Reagan supports. But he added that the administration could still seek to sever the assistance from the reconciliation bill.